ReliaWiki - User contributions [en]

File:Fmra occurrence scale large.png

2015-03-26T20:54:22Z

Chris Kahn: uploaded a new version of "File:Fmra occurrence scale large.png"

Template:WebNotes/DOEMixture Data

2015-02-24T22:16:02Z

Chris Kahn:

{{Template:NoSkin}}
{{Template: Web Notes DOE Banner}}
|{{Font|Mixture Design Folios|11|tahoma|bold|gray}}
Mixture designs are used to determine the best proportions of components to use in a mixture. They can also help you determine the best process variable settings to use (e.g., temperature).

|}
{{Font|Learn more from...|11|tahoma|bold|gray}}
{| border="0" align="left" cellpadding="0" cellspacing="3"
|-
| [[Image:Helpblue.png]]
| [http://help.synthesisplatform.net/doex/mixture_designs.htm the help file...]
|-
| [[Image:Book blue.png]]
| [http://www.reliawiki.org/index.php/Mixture_Design the theory textbook...]
|}

 
 
 
 
 
 
 
 
 
 

[[File:docedit.png|20px|right|link=http://www.reliawiki.org/index.php?title=Template:WebNotes/DOEMixture_Data&action=edit]]

Template:WebNotes/DOEMixture Data

2015-02-24T22:14:59Z

Chris Kahn: Created page with '{{Template:NoSkin}} {{Template: Web Notes DOE Banner}} |{{Font|Mixture Design Folios|11|tahoma|bold|gray}} Mixture designs are used to determine the best proportions of component…'

Webnotes Pages

2015-02-24T21:59:55Z

Chris Kahn: /* DOE++ */

This page provides a summary of the ReliaWiki.org pages that are linked from the "Reliability Web Notes" feature in ReliaSoft's Synthesis applications. To access this information from within the software, go to the Reliability Web Notes page in My Portal.

==Weibull++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Template:WebNotes/Weibull++ http://reliawiki.org/index.php/Template:WebNotes/Weibull++]
{|style="align:center" border="1"

|-
|One-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_1P-Weibull|| Weibull++ ||Standard
|-
|Two-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_2P-Weibull|| Weibull++ ||Standard
|-
|Three-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_3P-Weibull|| Weibull++ ||Standard
|-
|Mixed Weibull || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Mixed_Weibull Configured as a "template" so the same content can be used in pages that linked separately for each type of Prior distribution. The template page is "Mixed_Weibull" but the software links to "2_Subpop-Mixed_Weibull," "3_Subpop-Mixed_Weibull" and "4_Subpop-Mixed_Weibull"|| Weibull++ ||Standard
|-
|Bayesian Weibull|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_B-W Configured as a "template" so the same content can be used in pages that linked separately for each type of Prior distribution. Still negotiating with developers on whether the links will be changed in the software for 8.0.5 and beyond.|| Weibull++ ||Standard
|-
|1P Exponential|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_1P-Exponential ||Weibull++ ||Standard
|-
|2P Exponential|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_2P-Exponential ||Weibull++ ||Standard
|-
|Lognormal|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Lognormal|| Weibull++ ||Standard
|-
|Normal|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Normal|| Weibull++ ||Standard
|-
|Generalized Gamma|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Generalized_Gamma|| Weibull++ ||Standard
|-
|Gamma ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Gamma|| Weibull++ ||Standard
|-
|Logistic|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Logistic|| Weibull++ ||Standard
|-
|Loglogistic|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Loglogistic|| Weibull++ ||Standard
|-
|Gumbel|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Gumbel|| Weibull++ ||Standard
|-
|CFM|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_CFM Configured as a "template" so the same content can be used in pages that linked separately for each distribution. Still negotiating with developers on whether the links will be changed in the software for 8.0.5 and beyond.|| Weibull++ ||Standard

|-
|Weibull Degradation|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWeibull_Degradation_Data|| Weibull++ ||Degradation

|-
|Actuarial-Simple||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_ActuarialSimple||Weibull++||Non-parametric LDA
|-
|Kaplan Meier||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_KaplanMeier||Weibull++||Non-parametric LDA
|-
|Actuarial-Standard||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_ActuarialStandard||Weibull++||Non-parametric LDA
|-
|Non-parametric LDA Plot|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Plot|| Weibull++ ||Non-parametric LDA
|-
|Nevada folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Nevada|| Weibull++|| Warranty
|-
|Times-to-failure folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Weibull|| Weibull++ ||Warranty
|-
|Dates of failure folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_DateFailed|| Weibull++ ||Warranty
|-
|Usage folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Usage|| Weibull++|| Warranty

|-
|Event Log Folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEvent_Log_Folio || Weibull++ || Event Log
|-
| Non-Parametric RDA Data || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_RDA_Data || Weibull++ || Non-parametric RDA

|-
|Parametric RDA Data || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BParameteric_RDA_Data || Weibull++ || Parametric RDA

|-
| Equation Fit Solver || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEquation_Fit_Solver_Data || Weibull++ || Equation Fit Solver
|-
| Equation Fit Solver Plot || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEquation_Fit_Solver_Plot || Weibull++ || Equation Fit Solver
|-
| SimuMatic || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BSimuMatic_Data Configured as a "template" so the same content can be used in pages that were linked in 8.0.4 and below. || Weibull++|| SimuMatic

|-
|Target Reliability Estimator||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTarget_Reliability_Estimator||Weibull++||Target Reliability
|-
|General Spreadsheet|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio|| Weibull++|| Standard
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Plot|| Weibull++ || W++ Plot
|-
|Analysis Workbook || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BAnalysis_Workbook|| Weibull++|| Reports
|}

==Both Weibull++ and ALTA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Weibull++_ALTA http://reliawiki.org/index.php/Template:WebNotes/Weibull++_ALTA]
{|style="align:center" border="1"
|-
|Life Comparison||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BLife_Comparison||Weibull++ and ALTA||Life Comparison
|-
|Stress-Strength ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStress-Strength||Weibull++ and ALTA||Stress-Strength
|-
|Test Design Folio||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_RDT||Weibull++ and ALTA||Test Design Folio
|-
|Test Design RDT Plot Table|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_RDT_PlotTable|| Weibull++ and ALTA ||Test Design Folio
|-
|Test Design Expected Failure Time||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_Expected_Failure_Time||Weibull++ and ALTA||Test Design Folio
|-
|Test Design Difference Detection Matrix||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_Difference_Detection_Matrix||Weibull++ and ALTA||Test Design Folio

|-
|Diagram ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BDiagram||Weibull++ and ALTA||Diagram

|-
|Overlay Plot || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BOverlay_Plot_None ||Weibull++ and ALTA ||Overlay Plot

|-
|Side by Side Plot||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BSide-By-Side_Plot|| Weibull++ and ALTA|| Side-by-Side Plot
|-
|-
|Maintenance Planning Tool||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BMaintenance-Planning|| Weibull++ and ALTA|| Maintenance Planning Tool
|-
|}

==ALTA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Template:WebNotes/ALTA http://reliawiki.org/index.php/Template:WebNotes/ALTA]
{|style="align:center" border="1"
|-
|General Spreadsheet || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio ||ALTA ||Standard Folio
|-
|Standard Folio Arrhenius || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_Arrhenius|| ALTA|| Standard Folio
|-
|Standard Folio Eyring || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_Eyring|| ALTA|| Standard Folio
|-
|Standard Folio Inverse Power Law|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_PowerLaw|| ALTA|| Standard Folio
|-
|Standard Folio Temperature Humidity || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_TempHumidity ||ALTA ||Standard Folio
|-
|Standard Folio Temperature Non-Thermal || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_TempNonThermal|| ALTA ||Standard Folio
|-
|Standard Folio Generalized Eyring|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_GenEyring|| ALTA|| Standard Folio
|-
|Standard Folio Proportional Hazards || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_PHazards|| ALTA|| Standard Folio
|-
|Standard Folio General Log-Linear|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_GenModel|| ALTA|| Standard Folio
|-
|Standard Folio Cumulative Damage|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_CumDamage|| ALTA|| Standard Folio

|-
|ALTA Degradation|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Degradation_Data|| ALTA|| Degradation

|-
|Stress Profile || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAFolio|| ALTA ||Stress Profile
|-
|ALTA Test Plan || http://www.reliawiki.org/index.php/Template:WebNotes/ALTATest_Plan ||ALTA ||Test Plan
|-
|SimuMatic|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTASimumatic_Data Configured as a "template" so the same content can be used in pages that were linked in 8.0.4 and below. ||ALTA ||SimuMatic

|-
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/ALTAStandard_Folio_Plot|| ALTA || ALTA Plot
|-
|}

==BlockSim==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/BlockSim http://www.reliawiki.com/index.php/Template:WebNotes/BlockSim]
{|style="align:center" border="1"
|-
|Allocation Analysis || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAllocation_Analysis_Folio|| BlockSim|| Allocation Analysis
|-
|Analytical FRED|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_FRED_Report|| BlockSim || FRED Report
|-
|Simulation FRED || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_FRED_Report|| BlockSim|| FRED Report
|-
|Analysis Workbook|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalysis_Workbook ||BlockSim || Analysis Workbook
|-
|Analytical RBD || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_RBD_Diagram|| BlockSim ||Analytical RBD

|-
|Analytical Fault Tree|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_Fault_Tree_Diagram|| BlockSim ||Analytical Fault Tree
|-
|Simulation RBD|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_RBD_Diagram|| BlockSim ||Simulation RBD
|-
|Simulation Fault Tree|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_Fault_Tree_Diagram|| BlockSim ||Simulation Fault Tree
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimPlot||BlockSim||Plot Sheet
|-
|Overlay Plot||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimOverlay_Plot_None||BlockSim||Overlay Plot
|-
|Expert Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimExpert_Sheet||BlockSim||Expert Sheet
|-
|}

==Xfmea==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/Xfmea http://www.reliawiki.com/index.php/Template:WebNotes/Xfmea] 

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaSystemTree || Xfmea || System Tree
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaProperties|| Xfmea|| Item Properties
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaFMRA||Xfmea|| FMRA
|-
|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDFR || Xfmea || DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaRisk_Discovery_Questions || Xfmea || Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaRisk_Discovery_Ratings|| Xfmea || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaAnalysis_Plan || Xfmea || Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaPFD||Xfmea|| PFD
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaFMEA ||Xfmea|| FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDRBFM || Xfmea || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDVPR||Xfmea|| DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaControl_Plan||Xfmea|| Control Plan
|-

|}

==RCM++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/RCM http://www.reliawiki.com/index.php/Template:WebNotes/RCM]

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++SystemTree || RCM++|| System Tree
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Properties|| RCM++ || Item Properties
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++FMRA|| RCM++ || FMRA
|-
|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DFR || RCM++|| DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Risk_Discovery_Questions || RCM++|| Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Risk_Discovery_Ratings|| RCM++ || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Analysis_Plan || RCM++|| Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++PFD|| RCM++ || PFD
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++FMEA || RCM++ || FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DRBFM || RCM++ || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DVPR|| RCM++ || DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Control_Plan|| RCM++ || Control Plan

|-

|}

==RBI==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/RBI http://www.reliawiki.com/index.php/Template:WebNotes/RBI]

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/RBISystemTree || RBI || System Tree
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIFMRA|| RBI || FMRA
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/RBIProperties|| RBI || Item Properties
|-
|RBI General Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIGeneral_Properties || RBI || General Properties
|-
|RBI Damage Factors Selection ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDamage_Factors_Selection || RBI || Damage Factors Selection
|-
|RBI Damage Factor Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDamage_Factor_Properties || RBI || Damage Factor Properties
|-
|RBI Consequence Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIConsequence_Properties || RBI || Consequence Properties
|-
|RBI Results ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIResults || RBI || Results
|-
|RBI HexTubes ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIHexTube_Properties || RBI || HexTube properties
|-
|RBI Pressure Relief Devices||http://www.reliawiki.org/index.php/Template:WebNotes/RBIPressureRelief_Properties || RBI || Pressure Relief Devices
|-

|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/RBIDFR || RBI || DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIRisk_Discovery_Questions || RBI || Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/RBIRisk_Discovery_Ratings|| RBI || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/RBIAnalysis_Plan || RBI || Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/RBIPFD|| RBI || PFD Worksheet
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIFMEA || RBI || FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDRBFM || RBI || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDVPR|| RBI || DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIControl_Plan|| RBI || Control Plan
|-
|RBI Plots ||http://www.reliawiki.org/index.php/Template:WebNotes/RBI_Plot|| RBI || RBI Plots (V10 only)
|-
|}

==RGA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/RGA http://www.reliawiki.com/index.php/Template:WebNotes/RGA]

{|style="align:center" border="1"
| General Spreadsheet||http://www.reliawiki.org/index.php/Template:WebNotes/RGAGeneral_Spreadsheet||RGA||Standard
|-
| Duane Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGADuane||RGA||Standard
|-
| Crow-AMSAA Model for Developmental Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_AMSAA_Developmental||RGA||Standard
|-
| Crow-AMSAA Model for Fleet Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_AMSAA_Fleet||RGA||Standard
|-
| Crow Extended Model for Developmental Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Developmental||RGA||Standard
|-
| Crow Extended Model for Repairable Systems Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Repairable||RGA||Standard
|-
| Crow Extended Model for Fleet Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Fleet||RGA||Standard
|-
| Crow Extended-Continuous Evaluation Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Continuous||RGA||Standard
|-
| Lloyd-Lipow Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGALloyd-Lipow||RGA||Standard
|-
| Standard Gompertz Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAStandard_Gompertz||RGA||Standard
|-
| Modified Gompertz Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAModified_Gompertz||RGA||Standard
|-
| Logistic Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGALogistic||RGA||Standard
|-
| Power Law Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAPower_Law||RGA||Standard

|-
| Multi-Phase Plots||http://www.reliawiki.org/index.php/Template:WebNotes/RGAMultiPhase_Plot||RGA||Multi-Phase
|-
| Growth Planning Folio||http://www.reliawiki.org/index.php/Template:WebNotes/RGAGrowth_Planning||RGA||Growth Planning
|-
| Mission Profile Folio||http://www.reliawiki.org/index.php/Template:WebNotes/RGAMission_Profile||RGA||Mission Profile
|-
| RGA SimuMatic||http://www.reliawiki.org/index.php/Template:WebNotes/RGASimuMatic||RGA||SimuMatic
|-
| Repairable Systems Reliability Demonstration Tests||http://www.reliawiki.org/index.php/Template:WebNotes/RGARepairable_RDT||RGA||RDT

|-
| Plot Sheets in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAPlot||RGA||Plot Sheet
|-
| Overlay Plots in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAOverlay_Plot_None||RGA||Overlay
|-
| Side-by-Side Plots in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGASide-By-Side_Plot||RGA||Side-by-Side
|-
| Analysis Workbooks in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAAnalysis_Workbook||RGA||Analysis Workbook
|-
|}

==DOE++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/DOE http://www.reliawiki.com/index.php/Template:WebNotes/DOE]

{|style="align:center" border="1"
| Two Level Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOETwo_Level_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Plackett-Burman Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEPlackett_Burman_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| General Full Factorial Design||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGeneral_Full_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Taguchi OA Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOETaguchi_OA_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Central Composite Response Surface Method (RSM) Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOECentral_Composite_RSM||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Box-Behnken Response Surface Method (RSM) Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEBox_Behnken_RSM||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| One Factor Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOne_Factor||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Simplex Lattice Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimplex_Lattice||Mixture Design Folios
|-
| Simplex Centroid Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimplex_Centroid||Mixture Design Folios
|-
| Simplex Axial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimplex_Axial||Mixture Design Folios
|-
| Extreme Vertex Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEExtreme_Vertex||Mixture Design Folios
|-
| Robust Design Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOERobust_Data||Robust Design Folios -- show in Data tab
|-
| Mixture Design Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEMixture_Data||Mixture Design Folios -- show in Data tab
|-
| Free Form Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEFree_Form_Design||Free Form Folio
|-
| Multiple Linear Regression Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEMultiple_Linear_Regression||Multiple Linear Regression Folio
|-
| One-Way ANOVA Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEANOVA||One-Way Anova Folio
|-
| Linearity & Bias Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOELinearity_and_Bias||Linearity & Bias Folio
|-
| Gage Agreement Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGage_Agreement||Gage Agreement Folio
|-
| Gage R&R Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGage_R||Gage R&R Folio
|-
| Optimal Solution Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Optimal_Solution_Plot||Optimization Folio
|-
| Overlaid Contour Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Overlaid_Contour_Plot||Optimization Folio
|-
| Dynamic Overlaid Contour Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Dynamic_Overlaid_Contour_Plot||Optimization Folio
|-
| Plot Sheets in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOEPlot||Plot Sheet
|-
| Overlay Plots in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOverlay_Plot_None||Overlay Plot
|-
| Side-by-Side Plots in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOESide_By_Side_Plot||Side-by-Side Plot
|-
| Spreadsheets in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOESpreadsheet||Spreadsheet
|-
| Simulation Worksheets||http://www.reliawiki.org/index.php/Template:WebNotes/DOEExpert_Sheet||Simulation Worksheet
|-
|}

==RENO==
[http://reliawiki.org/index.php/Template:WebNotes/RENO http://reliawiki.org/index.php/Template:WebNotes/RENO]

'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

{|style="align:center" border="1"
|-
| RENO Flowcharts||http://www.reliawiki.org/index.php/Template:WebNotes/RENORENO_Flowchart_Flowchart||Flowchart
|-
| RENO Plot Sheets||http://www.reliawiki.org/index.php/Template:WebNotes/RENOPlot||Flowchart Plot Sheet
|-
|}

==Lambda Predict==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://reliawiki.org/index.php/Template:WebNotes/Lambda_Predict http://reliawiki.org/index.php/Template:WebNotes/Lambda_Predict]
{|style="align:center" border="1"
|-
|Generic ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictPrediction||Prediction Window - Blank hierarchy or Generic branch selected
|-
|MIL-217 Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictMIL-217||Prediction Window - MIL-217 Branch Selected
|-
| Bellcore/Telcordia Predictions||http://www.reliawiki.org/index.php/Template:WebNotes/PredictTelcordia||Prediction Window - Bellcore/Telcordia Branch Selected
|-
| NSWC (Mechanical) Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictNSWC||Prediction Window - NSWC Branch Selected
|-
| FIDES Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictFIDES||Prediction Window - FIDES Branch Selected
|-
| Derating||http://www.reliawiki.org/index.php/Template:WebNotes/PredictDerating||Select Derating Standard or Manage Derating Standard
|-
| Equal Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Equal||Allocation
|-
| AGREE Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_AGREE||Allocation
|-
| Feasibility of Objectives Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Feasibility||Allocation
|-
| ARINC Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_ARINC||Allocation
|-
| Repairable Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Repairable||Allocation
|-
| Plots in Lambda Predict||http://www.reliawiki.org/index.php/Template:WebNotes/PredictPlot||Plot Viewer
|-
| Import BOM||http://www.reliawiki.org/index.php/Template:WebNotes/PredictImport_BOM||Import BOM Wizard or Import Templates Window
|}

==MPC==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.org/index.php/Template:WebNotes/MPC http://www.reliawiki.org/index.php/Template:WebNotes/MPC]

{|style="align:center" border="1"
| System Hierarchy and MSI Selection||http://www.reliawiki.org/index.php/Template:WebNotes/MPCSystemHierarchy||System Hierarchy
|-
| F-F-E-C||http://www.reliawiki.org/index.php/Template:WebNotes/MPCFMEA||F-F-E-C
|-
| Structural Hierarchy and SSI Selection||http://www.reliawiki.org/index.php/Template:WebNotes/MPCStructuralHierarchy||Structural Hierarchy
|-
| Accidental Damage Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCAccidentalDamage||Accidental Damage Analysis (includes both Metals and Non-Metals)
|-
| Environmental Deterioration Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCEnvironmental_Deterioration||Environmental Deterioration Analysis
|-
| Zonal Hierarchy and Selecting Items for Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalHierarchy||Zonal Hierarchy
|-
| Standard Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalStandard||Standard Zonal Analysis
|-
| Enhanced Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalEnhanced||Enhanced Zonal Analysis
|-
| L/HIRF Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalLHIRF||Zonal L/HIRF Analysis
|-
| Fatigue Damage Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCFatigue_Damage||Fatigue Damage Analysis (V10 only)
|-

|}

==Retired Plot Type Descriptions Used in Version 8==
The following pages were used in Version 8 when the user selected a different plot type. In Version 9, the description will be directly available from an (i) icon in the plot control panel, so these pages are no longer needed.

{|style="align:center" border="1"
|-
|Contour Plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptContour|| Weibull++ || W++ Plot
|-
|Probability Weibull Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptProbability|| Weibull++ ||W++ Plot
|-
|Reliability vs. Time Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptReliability|| Weibull++ ||W++ Plot
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptUnreliability|| Weibull++ ||W++ Plot
|-
|pdf Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptPdf|| Weibull++ ||W++ Plot
|-
|Failure Rate vs. Time|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFailureRate|| Weibull++ ||W++ Plot
|-
|F/S Histogram|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSHistogram|| Weibull++ ||W++ Plot
|-
|F/S Pie|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSPie|| Weibull++ ||W++ Plot
|-
|F/S Timeline|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSTimeline|| Weibull++ ||W++ Plot
|-
|Degradation vs. time(linear) plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Weibull_Degradation_Plot_ptDegradationLinear|| Weibull++ ||Degradation
|-
|Degradation vs. time(log) plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Weibull_Degradation_Plot_ptDegradationLog|| Weibull++ ||Degradation
|-
|-
|Chi-Squared-Sales||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptChiSqSales||Weibull++||Warranty
|-
|Chi-Squared Returns||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptChiSqReturns||Weibull++||Warranty

|-
|Expected Failures||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptExpectedFailures|| Weibull++||Warranty
|-
|Overlay Plot Probability ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptProbability ||Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Reliability vs. Time|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptReliability|| Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Unreliability vs. Time || http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptUnreliability|| Weibull++ and ALTA|| Overlay Plot
|-
|Overlay Plot Pdf Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptPdf ||Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Failure Rate vs. Time ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptFailureRate|| Weibull++ and ALTA|| Overlay Plot
|-
|Overlay Plot Contour Plot || http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptContour ||Weibull++ and ALTA|| Overlay Plot
|-
| Non-parametric RDA folios (plot) ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Non-Parametric_RDA_Plot ||Weibull++ || Non-parametric RDA
|-
|Parametric RDA Plots|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot || Weibull++ || Parametric RDA
|-
|Parametric Cum. Number of Failures Plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CumNumFailures||Weibull++||Parametric RDA
|-
|Cum. Failure Intensity vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CumFI||Weibull++||Parametric RDA
|-
|Instant. Failure Intensity vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_InstFI||Weibull++||Parametric RDA
|-
|Cond. Reliability vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CondReliability||Weibull++||Parametric RDA
|-
|Cond. Unreliability vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CondUnreliability||Weibull++||Parametric RDA
|-
| Simumatic Plot || http://www.reliawiki.org/index.php/Weibull++_Simumatic_Plot || Weibull++ || SimuMatic
|-
|Diagram Reliability plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptReliability||Weibull++ and ALTA||Diagram
|-
|Diagram Unreliability plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptUnreliability||Weibull++ and ALTA||Diagram
|-
|Diagram Pdf||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptPdf ||Weibull++ and ALTA||Diagram
|-
|Diagram Failure Rate||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptFailureRate ||Weibull++ and ALTA||Diagram
|-
|Use Level Probability Weibull|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptUseLevel|| ALTA|| ALTA Plots
|-
|Reliability vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptReliability|| ALTA|| ALTA Plots
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptUnreliability|| ALTA|| ALTA Plots
|-
|Pdf Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptPdf|| ALTA|| ALTA Plots
|-
|Failure Rate vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptFailureRate|| ALTA|| ALTA Plots
|-
|Life vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptLifeStress|| ALTA|| ALTA Plots
|-
|STD vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStdDevStress|| ALTA|| ALTA Plots
|-
|AF vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptAFStress|| ALTA|| ALTA Plots
|-
|Cox-Snell Residual Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptCoxSnellResiduals|| ALTA|| ALTA Plots
|-
|Probability Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptProbability|| ALTA|| ALTA Plots
|-
|Standardized Residuals Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStandardResiduals|| ALTA|| ALTA Plots
|-
|Standardized vs. Fitted Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStandardFitted|| ALTA|| ALTA Plots
|-
|Degradation vs. time(linear) plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Degradation_Plot_ptDegradationLinear|| ALTA|| Degradation
|-
|Degradation vs. time(log) plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Degradation_Plot_ptDegradationLog|| ALTA|| Degradation
|-
|ALTA Simumatic Plot ||http://www.reliawiki.org/index.php/ALTA_Simumatic_Plot ||ALTA ||SimuMatic
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptUnreliability The analytical RBD plot notes were configured as "templates" so the same content can be used in the equivalent analytical fault tree plot pages that were linked in 8.0.4 and below.|| BlockSim|| Analytical RBD Plots
|-
|Reliability vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptReliability|| BlockSim ||Analytical RBD Plots
|-
|Pdf Plot ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptPdf|| BlockSim ||Analytical RBD Plots
|-
|Failure vs. Time plot ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptFailureRate|| BlockSim ||Analytical RBD Plots
|-
|RI vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptDynamicRI|| BlockSim ||Analytical RBD Plots
|-
|Static RI ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptStaticRI|| BlockSim ||Analytical RBD Plots
|-
|Static RI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptTableauRI|| BlockSim ||Analytical RBD Plots
|-
|Block Unreliability|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockUnreliability|| BlockSim ||Analytical RBD Plots
|-
|Block Reliability|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockReliability|| BlockSim ||Analytical RBD Plots
|-
|Block pdf|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockPdf|| BlockSim ||Analytical RBD Plots
|-
|Block Failure Rate|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockFailureRate|| BlockSim ||Analytical RBD Plots
|-
|RS FCI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSFCIBarChart The simulation RBD plot notes were configured as "templates" so the same content can be used in the equivalent simulation fault tree, FMRA and phase diagram plot pages that were linked in 8.0.4 and below.|| BlockSim ||Simulation RBD Plots
|-
|Point Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPointAvailability|| BlockSim ||Simulation RBD Plots
|-
|Point Reliability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPointReliability|| BlockSim ||Simulation RBD Plots
|-
|Point both A & R|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBothPointAR|| BlockSim ||Simulation RBD Plots
|-
|Cost|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCost|| BlockSim ||Simulation RBD Plots
|-
|Mean Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptMeanAvailability|| BlockSim ||Simulation RBD Plots
|-
|Point System Failures|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptSysFailures|| BlockSim ||Simulation RBD Plots
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptThroughput|| BlockSim ||Simulation RBD Plots
|-
|System Up/Down|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptSystemUpDown|| BlockSim ||Simulation RBD Plots
|-
|Block Up/Down|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockUpDown|| BlockSim ||Simulation RBD Plots
|-
|RS FCI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSFCITableau|| BlockSim ||Simulation RBD Plots
|-
|RS DECI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDECIBarChart|| BlockSim ||Simulation RBD Plots
|-
|RS DECI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDECITableau|| BlockSim ||Simulation RBD Plots
|-
|RS DTCI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDTCIBarChart|| BlockSim ||Simulation RBD Plots
|-
|RS DTCI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDTCITableau|| BlockSim ||Simulation RBD Plots
|-
|Block Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockAvailability|| BlockSim ||Simulation RBD Plots
|-
|Block Costs|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockCosts|| BlockSim ||Simulation RBD Plots
|-
|Block Downtime|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockDownTime|| BlockSim ||Simulation RBD Plots
|-
|Block Expected Failures|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExpectedFailures|| BlockSim ||Simulation RBD Plots
|-
|Expected Downing Events|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExpectedEvents|| BlockSim ||Simulation RBD Plots
|-
|Block ThroughPut|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockThroughPut|| BlockSim|| Simulation RBD Plots
|-
|Excess Capacity|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExcessCapacity|| BlockSim ||Simulation RBD Plots
|-
|Block Backlog|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockBackLog|| BlockSim ||Simulation RBD Plots
|-
|Backlog Processed|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockBackLogProcessed|| BlockSim ||Simulation RBD Plots
|-
|Block Results Bubble|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockResultsBubble|| BlockSim ||Simulation RBD Plots
|-

|Simulation RBD Plot Crew Accepted Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewAcceptedCalls ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Rejected Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewRejectedCalls|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Costs || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewCrewCosts ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Time Used || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewTimeUsed ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Average Stock Level || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolAverageStockLevel ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Items Dispensed || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolItemsDispensed|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Average Time To Dispense || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolAverageTimeToDispense|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Rejected Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolRejectedCalls|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Emergency Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolEmergingCalls|| BlockSim ||Simulation RBD Plots
|-
|Simulation RBD Plot Pool Costs ||http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolCosts ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Cost Per Item ||http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolCostPerItem|| BlockSim ||Simulation RBD Plots
|-
|Simulation Fault Tree Diagram||http://www.reliawiki.org/index.php/BlockSim_Simulation_Fault_Tree_Diagram||BlockSim||Simulation Fault Tree
|-
|Phase Diagram|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Diagram|| BlockSim ||Phase Diagram
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemThroughPut ||BlockSim ||Phase Diagram Plots (Unique)
|-
|Expected Events|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemExpectedEvents ||BlockSim ||Phase Diagram Plots (Unique)
|-
|System Expected Failures|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemExpectedFailures|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Downtime|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemDownTime|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Costs|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemCosts|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Availability|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemAvailability|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Availability-All Events|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemAvailability_AllEvents|| BlockSim ||Phase Diagram Plots (Unique)
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptUnreliability|| BlockSim ||Overlay Plot Analytical
|-
|Reliability vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptReliability|| BlockSim|| Overlay Plot Analytical
|-
|Pdf Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPdf|| BlockSim ||Overlay Plot Analytical
|-
|Failure Rate vs. Time|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptFailureRate|| BlockSim ||Overlay Plot Analytical
|-
|Point Availability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPointAvailability|| BlockSim ||Overlay Plot Simulation
|-
|Point Reliability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPointReliability|| BlockSim ||Overlay Plot Simulation
|-
|Cost|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptCost|| BlockSim ||Overlay Plot Simulation
|-
|Mean Availability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptMeanAvailability|| BlockSim ||Overlay Plot Simulation
|-
|System Failures|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptSysFailures|| BlockSim ||Overlay Plot Simulation
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptThroughput|| BlockSim ||Overlay Plot Simulation
|-
|System Bubble Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptSystemResultsBubble|| BlockSim ||Overlay Plot Simulation

|-
|Overlay Plot || http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot|| BlockSim|| Overlay Plot

|-
|Overlay Plot Reliability vs. Time (for mixed diagrams)|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptMixedMultiplotReliability|| BlockSim ||Overlay Plot
|}

[[Category: List of Webnotes Pages]]

Webnotes Pages

2015-02-24T21:57:23Z

Chris Kahn: /* DOE++ */

This page provides a summary of the ReliaWiki.org pages that are linked from the "Reliability Web Notes" feature in ReliaSoft's Synthesis applications. To access this information from within the software, go to the Reliability Web Notes page in My Portal.

==Weibull++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Template:WebNotes/Weibull++ http://reliawiki.org/index.php/Template:WebNotes/Weibull++]
{|style="align:center" border="1"

|-
|One-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_1P-Weibull|| Weibull++ ||Standard
|-
|Two-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_2P-Weibull|| Weibull++ ||Standard
|-
|Three-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_3P-Weibull|| Weibull++ ||Standard
|-
|Mixed Weibull || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Mixed_Weibull Configured as a "template" so the same content can be used in pages that linked separately for each type of Prior distribution. The template page is "Mixed_Weibull" but the software links to "2_Subpop-Mixed_Weibull," "3_Subpop-Mixed_Weibull" and "4_Subpop-Mixed_Weibull"|| Weibull++ ||Standard
|-
|Bayesian Weibull|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_B-W Configured as a "template" so the same content can be used in pages that linked separately for each type of Prior distribution. Still negotiating with developers on whether the links will be changed in the software for 8.0.5 and beyond.|| Weibull++ ||Standard
|-
|1P Exponential|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_1P-Exponential ||Weibull++ ||Standard
|-
|2P Exponential|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_2P-Exponential ||Weibull++ ||Standard
|-
|Lognormal|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Lognormal|| Weibull++ ||Standard
|-
|Normal|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Normal|| Weibull++ ||Standard
|-
|Generalized Gamma|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Generalized_Gamma|| Weibull++ ||Standard
|-
|Gamma ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Gamma|| Weibull++ ||Standard
|-
|Logistic|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Logistic|| Weibull++ ||Standard
|-
|Loglogistic|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Loglogistic|| Weibull++ ||Standard
|-
|Gumbel|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Gumbel|| Weibull++ ||Standard
|-
|CFM|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_CFM Configured as a "template" so the same content can be used in pages that linked separately for each distribution. Still negotiating with developers on whether the links will be changed in the software for 8.0.5 and beyond.|| Weibull++ ||Standard

|-
|Weibull Degradation|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWeibull_Degradation_Data|| Weibull++ ||Degradation

|-
|Actuarial-Simple||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_ActuarialSimple||Weibull++||Non-parametric LDA
|-
|Kaplan Meier||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_KaplanMeier||Weibull++||Non-parametric LDA
|-
|Actuarial-Standard||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_ActuarialStandard||Weibull++||Non-parametric LDA
|-
|Non-parametric LDA Plot|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Plot|| Weibull++ ||Non-parametric LDA
|-
|Nevada folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Nevada|| Weibull++|| Warranty
|-
|Times-to-failure folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Weibull|| Weibull++ ||Warranty
|-
|Dates of failure folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_DateFailed|| Weibull++ ||Warranty
|-
|Usage folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Usage|| Weibull++|| Warranty

|-
|Event Log Folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEvent_Log_Folio || Weibull++ || Event Log
|-
| Non-Parametric RDA Data || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_RDA_Data || Weibull++ || Non-parametric RDA

|-
|Parametric RDA Data || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BParameteric_RDA_Data || Weibull++ || Parametric RDA

|-
| Equation Fit Solver || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEquation_Fit_Solver_Data || Weibull++ || Equation Fit Solver
|-
| Equation Fit Solver Plot || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEquation_Fit_Solver_Plot || Weibull++ || Equation Fit Solver
|-
| SimuMatic || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BSimuMatic_Data Configured as a "template" so the same content can be used in pages that were linked in 8.0.4 and below. || Weibull++|| SimuMatic

|-
|Target Reliability Estimator||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTarget_Reliability_Estimator||Weibull++||Target Reliability
|-
|General Spreadsheet|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio|| Weibull++|| Standard
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Plot|| Weibull++ || W++ Plot
|-
|Analysis Workbook || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BAnalysis_Workbook|| Weibull++|| Reports
|}

==Both Weibull++ and ALTA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Weibull++_ALTA http://reliawiki.org/index.php/Template:WebNotes/Weibull++_ALTA]
{|style="align:center" border="1"
|-
|Life Comparison||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BLife_Comparison||Weibull++ and ALTA||Life Comparison
|-
|Stress-Strength ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStress-Strength||Weibull++ and ALTA||Stress-Strength
|-
|Test Design Folio||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_RDT||Weibull++ and ALTA||Test Design Folio
|-
|Test Design RDT Plot Table|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_RDT_PlotTable|| Weibull++ and ALTA ||Test Design Folio
|-
|Test Design Expected Failure Time||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_Expected_Failure_Time||Weibull++ and ALTA||Test Design Folio
|-
|Test Design Difference Detection Matrix||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_Difference_Detection_Matrix||Weibull++ and ALTA||Test Design Folio

|-
|Diagram ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BDiagram||Weibull++ and ALTA||Diagram

|-
|Overlay Plot || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BOverlay_Plot_None ||Weibull++ and ALTA ||Overlay Plot

|-
|Side by Side Plot||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BSide-By-Side_Plot|| Weibull++ and ALTA|| Side-by-Side Plot
|-
|-
|Maintenance Planning Tool||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BMaintenance-Planning|| Weibull++ and ALTA|| Maintenance Planning Tool
|-
|}

==ALTA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Template:WebNotes/ALTA http://reliawiki.org/index.php/Template:WebNotes/ALTA]
{|style="align:center" border="1"
|-
|General Spreadsheet || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio ||ALTA ||Standard Folio
|-
|Standard Folio Arrhenius || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_Arrhenius|| ALTA|| Standard Folio
|-
|Standard Folio Eyring || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_Eyring|| ALTA|| Standard Folio
|-
|Standard Folio Inverse Power Law|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_PowerLaw|| ALTA|| Standard Folio
|-
|Standard Folio Temperature Humidity || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_TempHumidity ||ALTA ||Standard Folio
|-
|Standard Folio Temperature Non-Thermal || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_TempNonThermal|| ALTA ||Standard Folio
|-
|Standard Folio Generalized Eyring|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_GenEyring|| ALTA|| Standard Folio
|-
|Standard Folio Proportional Hazards || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_PHazards|| ALTA|| Standard Folio
|-
|Standard Folio General Log-Linear|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_GenModel|| ALTA|| Standard Folio
|-
|Standard Folio Cumulative Damage|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_CumDamage|| ALTA|| Standard Folio

|-
|ALTA Degradation|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Degradation_Data|| ALTA|| Degradation

|-
|Stress Profile || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAFolio|| ALTA ||Stress Profile
|-
|ALTA Test Plan || http://www.reliawiki.org/index.php/Template:WebNotes/ALTATest_Plan ||ALTA ||Test Plan
|-
|SimuMatic|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTASimumatic_Data Configured as a "template" so the same content can be used in pages that were linked in 8.0.4 and below. ||ALTA ||SimuMatic

|-
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/ALTAStandard_Folio_Plot|| ALTA || ALTA Plot
|-
|}

==BlockSim==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/BlockSim http://www.reliawiki.com/index.php/Template:WebNotes/BlockSim]
{|style="align:center" border="1"
|-
|Allocation Analysis || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAllocation_Analysis_Folio|| BlockSim|| Allocation Analysis
|-
|Analytical FRED|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_FRED_Report|| BlockSim || FRED Report
|-
|Simulation FRED || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_FRED_Report|| BlockSim|| FRED Report
|-
|Analysis Workbook|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalysis_Workbook ||BlockSim || Analysis Workbook
|-
|Analytical RBD || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_RBD_Diagram|| BlockSim ||Analytical RBD

|-
|Analytical Fault Tree|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_Fault_Tree_Diagram|| BlockSim ||Analytical Fault Tree
|-
|Simulation RBD|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_RBD_Diagram|| BlockSim ||Simulation RBD
|-
|Simulation Fault Tree|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_Fault_Tree_Diagram|| BlockSim ||Simulation Fault Tree
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimPlot||BlockSim||Plot Sheet
|-
|Overlay Plot||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimOverlay_Plot_None||BlockSim||Overlay Plot
|-
|Expert Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimExpert_Sheet||BlockSim||Expert Sheet
|-
|}

==Xfmea==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/Xfmea http://www.reliawiki.com/index.php/Template:WebNotes/Xfmea] 

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaSystemTree || Xfmea || System Tree
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaProperties|| Xfmea|| Item Properties
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaFMRA||Xfmea|| FMRA
|-
|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDFR || Xfmea || DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaRisk_Discovery_Questions || Xfmea || Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaRisk_Discovery_Ratings|| Xfmea || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaAnalysis_Plan || Xfmea || Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaPFD||Xfmea|| PFD
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaFMEA ||Xfmea|| FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDRBFM || Xfmea || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDVPR||Xfmea|| DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaControl_Plan||Xfmea|| Control Plan
|-

|}

==RCM++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/RCM http://www.reliawiki.com/index.php/Template:WebNotes/RCM]

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++SystemTree || RCM++|| System Tree
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Properties|| RCM++ || Item Properties
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++FMRA|| RCM++ || FMRA
|-
|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DFR || RCM++|| DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Risk_Discovery_Questions || RCM++|| Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Risk_Discovery_Ratings|| RCM++ || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Analysis_Plan || RCM++|| Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++PFD|| RCM++ || PFD
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++FMEA || RCM++ || FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DRBFM || RCM++ || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DVPR|| RCM++ || DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Control_Plan|| RCM++ || Control Plan

|-

|}

==RBI==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/RBI http://www.reliawiki.com/index.php/Template:WebNotes/RBI]

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/RBISystemTree || RBI || System Tree
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIFMRA|| RBI || FMRA
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/RBIProperties|| RBI || Item Properties
|-
|RBI General Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIGeneral_Properties || RBI || General Properties
|-
|RBI Damage Factors Selection ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDamage_Factors_Selection || RBI || Damage Factors Selection
|-
|RBI Damage Factor Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDamage_Factor_Properties || RBI || Damage Factor Properties
|-
|RBI Consequence Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIConsequence_Properties || RBI || Consequence Properties
|-
|RBI Results ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIResults || RBI || Results
|-
|RBI HexTubes ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIHexTube_Properties || RBI || HexTube properties
|-
|RBI Pressure Relief Devices||http://www.reliawiki.org/index.php/Template:WebNotes/RBIPressureRelief_Properties || RBI || Pressure Relief Devices
|-

|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/RBIDFR || RBI || DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIRisk_Discovery_Questions || RBI || Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/RBIRisk_Discovery_Ratings|| RBI || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/RBIAnalysis_Plan || RBI || Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/RBIPFD|| RBI || PFD Worksheet
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIFMEA || RBI || FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDRBFM || RBI || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDVPR|| RBI || DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIControl_Plan|| RBI || Control Plan
|-
|RBI Plots ||http://www.reliawiki.org/index.php/Template:WebNotes/RBI_Plot|| RBI || RBI Plots (V10 only)
|-
|}

==RGA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/RGA http://www.reliawiki.com/index.php/Template:WebNotes/RGA]

{|style="align:center" border="1"
| General Spreadsheet||http://www.reliawiki.org/index.php/Template:WebNotes/RGAGeneral_Spreadsheet||RGA||Standard
|-
| Duane Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGADuane||RGA||Standard
|-
| Crow-AMSAA Model for Developmental Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_AMSAA_Developmental||RGA||Standard
|-
| Crow-AMSAA Model for Fleet Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_AMSAA_Fleet||RGA||Standard
|-
| Crow Extended Model for Developmental Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Developmental||RGA||Standard
|-
| Crow Extended Model for Repairable Systems Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Repairable||RGA||Standard
|-
| Crow Extended Model for Fleet Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Fleet||RGA||Standard
|-
| Crow Extended-Continuous Evaluation Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Continuous||RGA||Standard
|-
| Lloyd-Lipow Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGALloyd-Lipow||RGA||Standard
|-
| Standard Gompertz Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAStandard_Gompertz||RGA||Standard
|-
| Modified Gompertz Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAModified_Gompertz||RGA||Standard
|-
| Logistic Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGALogistic||RGA||Standard
|-
| Power Law Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAPower_Law||RGA||Standard

|-
| Multi-Phase Plots||http://www.reliawiki.org/index.php/Template:WebNotes/RGAMultiPhase_Plot||RGA||Multi-Phase
|-
| Growth Planning Folio||http://www.reliawiki.org/index.php/Template:WebNotes/RGAGrowth_Planning||RGA||Growth Planning
|-
| Mission Profile Folio||http://www.reliawiki.org/index.php/Template:WebNotes/RGAMission_Profile||RGA||Mission Profile
|-
| RGA SimuMatic||http://www.reliawiki.org/index.php/Template:WebNotes/RGASimuMatic||RGA||SimuMatic
|-
| Repairable Systems Reliability Demonstration Tests||http://www.reliawiki.org/index.php/Template:WebNotes/RGARepairable_RDT||RGA||RDT

|-
| Plot Sheets in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAPlot||RGA||Plot Sheet
|-
| Overlay Plots in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAOverlay_Plot_None||RGA||Overlay
|-
| Side-by-Side Plots in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGASide-By-Side_Plot||RGA||Side-by-Side
|-
| Analysis Workbooks in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAAnalysis_Workbook||RGA||Analysis Workbook
|-
|}

==DOE++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/DOE http://www.reliawiki.com/index.php/Template:WebNotes/DOE]

{|style="align:center" border="1"
| Two Level Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOETwo_Level_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Plackett-Burman Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEPlackett_Burman_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| General Full Factorial Design||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGeneral_Full_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Taguchi OA Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOETaguchi_OA_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Central Composite Response Surface Method (RSM) Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOECentral_Composite_RSM||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Box-Behnken Response Surface Method (RSM) Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEBox_Behnken_RSM||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| One Factor Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOne_Factor||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Simplex Lattice Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimplex_Lattice||Mixture Design Folios
|-
| Simplex Centroid Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimplex_Centroid||Mixture Design Folios
|-
| Simplex Axial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimplex_Axial||Mixture Design Folios
|-
| Extreme Vertex Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEExtreme_Vertex||Mixture Design Folios
|-
| Robust Design Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOERobust_Data||Robust Design Folios -- show in all tabs except "Design"
|-
| Free Form Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEFree_Form_Design||Free Form Folio
|-
| Multiple Linear Regression Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEMultiple_Linear_Regression||Multiple Linear Regression Folio
|-
| One-Way ANOVA Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEANOVA||One-Way Anova Folio
|-
| Linearity & Bias Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOELinearity_and_Bias||Linearity & Bias Folio
|-
| Gage Agreement Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGage_Agreement||Gage Agreement Folio
|-
| Gage R&R Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGage_R||Gage R&R Folio
|-
| Optimal Solution Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Optimal_Solution_Plot||Optimization Folio
|-
| Overlaid Contour Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Overlaid_Contour_Plot||Optimization Folio
|-
| Dynamic Overlaid Contour Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Dynamic_Overlaid_Contour_Plot||Optimization Folio
|-
| Plot Sheets in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOEPlot||Plot Sheet
|-
| Overlay Plots in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOverlay_Plot_None||Overlay Plot
|-
| Side-by-Side Plots in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOESide_By_Side_Plot||Side-by-Side Plot
|-
| Spreadsheets in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOESpreadsheet||Spreadsheet
|-
| Simulation Worksheets||http://www.reliawiki.org/index.php/Template:WebNotes/DOEExpert_Sheet||Simulation Worksheet
|-
|}

==RENO==
[http://reliawiki.org/index.php/Template:WebNotes/RENO http://reliawiki.org/index.php/Template:WebNotes/RENO]

'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

{|style="align:center" border="1"
|-
| RENO Flowcharts||http://www.reliawiki.org/index.php/Template:WebNotes/RENORENO_Flowchart_Flowchart||Flowchart
|-
| RENO Plot Sheets||http://www.reliawiki.org/index.php/Template:WebNotes/RENOPlot||Flowchart Plot Sheet
|-
|}

==Lambda Predict==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://reliawiki.org/index.php/Template:WebNotes/Lambda_Predict http://reliawiki.org/index.php/Template:WebNotes/Lambda_Predict]
{|style="align:center" border="1"
|-
|Generic ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictPrediction||Prediction Window - Blank hierarchy or Generic branch selected
|-
|MIL-217 Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictMIL-217||Prediction Window - MIL-217 Branch Selected
|-
| Bellcore/Telcordia Predictions||http://www.reliawiki.org/index.php/Template:WebNotes/PredictTelcordia||Prediction Window - Bellcore/Telcordia Branch Selected
|-
| NSWC (Mechanical) Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictNSWC||Prediction Window - NSWC Branch Selected
|-
| FIDES Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictFIDES||Prediction Window - FIDES Branch Selected
|-
| Derating||http://www.reliawiki.org/index.php/Template:WebNotes/PredictDerating||Select Derating Standard or Manage Derating Standard
|-
| Equal Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Equal||Allocation
|-
| AGREE Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_AGREE||Allocation
|-
| Feasibility of Objectives Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Feasibility||Allocation
|-
| ARINC Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_ARINC||Allocation
|-
| Repairable Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Repairable||Allocation
|-
| Plots in Lambda Predict||http://www.reliawiki.org/index.php/Template:WebNotes/PredictPlot||Plot Viewer
|-
| Import BOM||http://www.reliawiki.org/index.php/Template:WebNotes/PredictImport_BOM||Import BOM Wizard or Import Templates Window
|}

==MPC==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.org/index.php/Template:WebNotes/MPC http://www.reliawiki.org/index.php/Template:WebNotes/MPC]

{|style="align:center" border="1"
| System Hierarchy and MSI Selection||http://www.reliawiki.org/index.php/Template:WebNotes/MPCSystemHierarchy||System Hierarchy
|-
| F-F-E-C||http://www.reliawiki.org/index.php/Template:WebNotes/MPCFMEA||F-F-E-C
|-
| Structural Hierarchy and SSI Selection||http://www.reliawiki.org/index.php/Template:WebNotes/MPCStructuralHierarchy||Structural Hierarchy
|-
| Accidental Damage Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCAccidentalDamage||Accidental Damage Analysis (includes both Metals and Non-Metals)
|-
| Environmental Deterioration Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCEnvironmental_Deterioration||Environmental Deterioration Analysis
|-
| Zonal Hierarchy and Selecting Items for Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalHierarchy||Zonal Hierarchy
|-
| Standard Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalStandard||Standard Zonal Analysis
|-
| Enhanced Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalEnhanced||Enhanced Zonal Analysis
|-
| L/HIRF Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalLHIRF||Zonal L/HIRF Analysis
|-
| Fatigue Damage Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCFatigue_Damage||Fatigue Damage Analysis (V10 only)
|-

|}

==Retired Plot Type Descriptions Used in Version 8==
The following pages were used in Version 8 when the user selected a different plot type. In Version 9, the description will be directly available from an (i) icon in the plot control panel, so these pages are no longer needed.

{|style="align:center" border="1"
|-
|Contour Plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptContour|| Weibull++ || W++ Plot
|-
|Probability Weibull Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptProbability|| Weibull++ ||W++ Plot
|-
|Reliability vs. Time Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptReliability|| Weibull++ ||W++ Plot
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptUnreliability|| Weibull++ ||W++ Plot
|-
|pdf Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptPdf|| Weibull++ ||W++ Plot
|-
|Failure Rate vs. Time|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFailureRate|| Weibull++ ||W++ Plot
|-
|F/S Histogram|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSHistogram|| Weibull++ ||W++ Plot
|-
|F/S Pie|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSPie|| Weibull++ ||W++ Plot
|-
|F/S Timeline|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSTimeline|| Weibull++ ||W++ Plot
|-
|Degradation vs. time(linear) plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Weibull_Degradation_Plot_ptDegradationLinear|| Weibull++ ||Degradation
|-
|Degradation vs. time(log) plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Weibull_Degradation_Plot_ptDegradationLog|| Weibull++ ||Degradation
|-
|-
|Chi-Squared-Sales||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptChiSqSales||Weibull++||Warranty
|-
|Chi-Squared Returns||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptChiSqReturns||Weibull++||Warranty

|-
|Expected Failures||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptExpectedFailures|| Weibull++||Warranty
|-
|Overlay Plot Probability ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptProbability ||Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Reliability vs. Time|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptReliability|| Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Unreliability vs. Time || http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptUnreliability|| Weibull++ and ALTA|| Overlay Plot
|-
|Overlay Plot Pdf Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptPdf ||Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Failure Rate vs. Time ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptFailureRate|| Weibull++ and ALTA|| Overlay Plot
|-
|Overlay Plot Contour Plot || http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptContour ||Weibull++ and ALTA|| Overlay Plot
|-
| Non-parametric RDA folios (plot) ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Non-Parametric_RDA_Plot ||Weibull++ || Non-parametric RDA
|-
|Parametric RDA Plots|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot || Weibull++ || Parametric RDA
|-
|Parametric Cum. Number of Failures Plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CumNumFailures||Weibull++||Parametric RDA
|-
|Cum. Failure Intensity vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CumFI||Weibull++||Parametric RDA
|-
|Instant. Failure Intensity vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_InstFI||Weibull++||Parametric RDA
|-
|Cond. Reliability vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CondReliability||Weibull++||Parametric RDA
|-
|Cond. Unreliability vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CondUnreliability||Weibull++||Parametric RDA
|-
| Simumatic Plot || http://www.reliawiki.org/index.php/Weibull++_Simumatic_Plot || Weibull++ || SimuMatic
|-
|Diagram Reliability plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptReliability||Weibull++ and ALTA||Diagram
|-
|Diagram Unreliability plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptUnreliability||Weibull++ and ALTA||Diagram
|-
|Diagram Pdf||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptPdf ||Weibull++ and ALTA||Diagram
|-
|Diagram Failure Rate||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptFailureRate ||Weibull++ and ALTA||Diagram
|-
|Use Level Probability Weibull|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptUseLevel|| ALTA|| ALTA Plots
|-
|Reliability vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptReliability|| ALTA|| ALTA Plots
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptUnreliability|| ALTA|| ALTA Plots
|-
|Pdf Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptPdf|| ALTA|| ALTA Plots
|-
|Failure Rate vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptFailureRate|| ALTA|| ALTA Plots
|-
|Life vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptLifeStress|| ALTA|| ALTA Plots
|-
|STD vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStdDevStress|| ALTA|| ALTA Plots
|-
|AF vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptAFStress|| ALTA|| ALTA Plots
|-
|Cox-Snell Residual Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptCoxSnellResiduals|| ALTA|| ALTA Plots
|-
|Probability Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptProbability|| ALTA|| ALTA Plots
|-
|Standardized Residuals Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStandardResiduals|| ALTA|| ALTA Plots
|-
|Standardized vs. Fitted Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStandardFitted|| ALTA|| ALTA Plots
|-
|Degradation vs. time(linear) plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Degradation_Plot_ptDegradationLinear|| ALTA|| Degradation
|-
|Degradation vs. time(log) plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Degradation_Plot_ptDegradationLog|| ALTA|| Degradation
|-
|ALTA Simumatic Plot ||http://www.reliawiki.org/index.php/ALTA_Simumatic_Plot ||ALTA ||SimuMatic
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptUnreliability The analytical RBD plot notes were configured as "templates" so the same content can be used in the equivalent analytical fault tree plot pages that were linked in 8.0.4 and below.|| BlockSim|| Analytical RBD Plots
|-
|Reliability vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptReliability|| BlockSim ||Analytical RBD Plots
|-
|Pdf Plot ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptPdf|| BlockSim ||Analytical RBD Plots
|-
|Failure vs. Time plot ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptFailureRate|| BlockSim ||Analytical RBD Plots
|-
|RI vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptDynamicRI|| BlockSim ||Analytical RBD Plots
|-
|Static RI ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptStaticRI|| BlockSim ||Analytical RBD Plots
|-
|Static RI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptTableauRI|| BlockSim ||Analytical RBD Plots
|-
|Block Unreliability|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockUnreliability|| BlockSim ||Analytical RBD Plots
|-
|Block Reliability|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockReliability|| BlockSim ||Analytical RBD Plots
|-
|Block pdf|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockPdf|| BlockSim ||Analytical RBD Plots
|-
|Block Failure Rate|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockFailureRate|| BlockSim ||Analytical RBD Plots
|-
|RS FCI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSFCIBarChart The simulation RBD plot notes were configured as "templates" so the same content can be used in the equivalent simulation fault tree, FMRA and phase diagram plot pages that were linked in 8.0.4 and below.|| BlockSim ||Simulation RBD Plots
|-
|Point Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPointAvailability|| BlockSim ||Simulation RBD Plots
|-
|Point Reliability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPointReliability|| BlockSim ||Simulation RBD Plots
|-
|Point both A & R|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBothPointAR|| BlockSim ||Simulation RBD Plots
|-
|Cost|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCost|| BlockSim ||Simulation RBD Plots
|-
|Mean Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptMeanAvailability|| BlockSim ||Simulation RBD Plots
|-
|Point System Failures|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptSysFailures|| BlockSim ||Simulation RBD Plots
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptThroughput|| BlockSim ||Simulation RBD Plots
|-
|System Up/Down|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptSystemUpDown|| BlockSim ||Simulation RBD Plots
|-
|Block Up/Down|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockUpDown|| BlockSim ||Simulation RBD Plots
|-
|RS FCI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSFCITableau|| BlockSim ||Simulation RBD Plots
|-
|RS DECI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDECIBarChart|| BlockSim ||Simulation RBD Plots
|-
|RS DECI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDECITableau|| BlockSim ||Simulation RBD Plots
|-
|RS DTCI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDTCIBarChart|| BlockSim ||Simulation RBD Plots
|-
|RS DTCI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDTCITableau|| BlockSim ||Simulation RBD Plots
|-
|Block Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockAvailability|| BlockSim ||Simulation RBD Plots
|-
|Block Costs|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockCosts|| BlockSim ||Simulation RBD Plots
|-
|Block Downtime|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockDownTime|| BlockSim ||Simulation RBD Plots
|-
|Block Expected Failures|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExpectedFailures|| BlockSim ||Simulation RBD Plots
|-
|Expected Downing Events|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExpectedEvents|| BlockSim ||Simulation RBD Plots
|-
|Block ThroughPut|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockThroughPut|| BlockSim|| Simulation RBD Plots
|-
|Excess Capacity|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExcessCapacity|| BlockSim ||Simulation RBD Plots
|-
|Block Backlog|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockBackLog|| BlockSim ||Simulation RBD Plots
|-
|Backlog Processed|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockBackLogProcessed|| BlockSim ||Simulation RBD Plots
|-
|Block Results Bubble|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockResultsBubble|| BlockSim ||Simulation RBD Plots
|-

|Simulation RBD Plot Crew Accepted Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewAcceptedCalls ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Rejected Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewRejectedCalls|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Costs || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewCrewCosts ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Time Used || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewTimeUsed ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Average Stock Level || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolAverageStockLevel ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Items Dispensed || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolItemsDispensed|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Average Time To Dispense || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolAverageTimeToDispense|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Rejected Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolRejectedCalls|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Emergency Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolEmergingCalls|| BlockSim ||Simulation RBD Plots
|-
|Simulation RBD Plot Pool Costs ||http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolCosts ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Cost Per Item ||http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolCostPerItem|| BlockSim ||Simulation RBD Plots
|-
|Simulation Fault Tree Diagram||http://www.reliawiki.org/index.php/BlockSim_Simulation_Fault_Tree_Diagram||BlockSim||Simulation Fault Tree
|-
|Phase Diagram|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Diagram|| BlockSim ||Phase Diagram
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemThroughPut ||BlockSim ||Phase Diagram Plots (Unique)
|-
|Expected Events|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemExpectedEvents ||BlockSim ||Phase Diagram Plots (Unique)
|-
|System Expected Failures|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemExpectedFailures|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Downtime|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemDownTime|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Costs|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemCosts|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Availability|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemAvailability|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Availability-All Events|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemAvailability_AllEvents|| BlockSim ||Phase Diagram Plots (Unique)
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptUnreliability|| BlockSim ||Overlay Plot Analytical
|-
|Reliability vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptReliability|| BlockSim|| Overlay Plot Analytical
|-
|Pdf Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPdf|| BlockSim ||Overlay Plot Analytical
|-
|Failure Rate vs. Time|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptFailureRate|| BlockSim ||Overlay Plot Analytical
|-
|Point Availability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPointAvailability|| BlockSim ||Overlay Plot Simulation
|-
|Point Reliability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPointReliability|| BlockSim ||Overlay Plot Simulation
|-
|Cost|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptCost|| BlockSim ||Overlay Plot Simulation
|-
|Mean Availability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptMeanAvailability|| BlockSim ||Overlay Plot Simulation
|-
|System Failures|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptSysFailures|| BlockSim ||Overlay Plot Simulation
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptThroughput|| BlockSim ||Overlay Plot Simulation
|-
|System Bubble Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptSystemResultsBubble|| BlockSim ||Overlay Plot Simulation

|-
|Overlay Plot || http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot|| BlockSim|| Overlay Plot

|-
|Overlay Plot Reliability vs. Time (for mixed diagrams)|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptMixedMultiplotReliability|| BlockSim ||Overlay Plot
|}

[[Category: List of Webnotes Pages]]

Webnotes Pages

2015-02-24T21:56:55Z

Chris Kahn: /* DOE++ */

This page provides a summary of the ReliaWiki.org pages that are linked from the "Reliability Web Notes" feature in ReliaSoft's Synthesis applications. To access this information from within the software, go to the Reliability Web Notes page in My Portal.

==Weibull++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Template:WebNotes/Weibull++ http://reliawiki.org/index.php/Template:WebNotes/Weibull++]
{|style="align:center" border="1"

|-
|One-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_1P-Weibull|| Weibull++ ||Standard
|-
|Two-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_2P-Weibull|| Weibull++ ||Standard
|-
|Three-Parameter Weibull Distribution|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_3P-Weibull|| Weibull++ ||Standard
|-
|Mixed Weibull || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Mixed_Weibull Configured as a "template" so the same content can be used in pages that linked separately for each type of Prior distribution. The template page is "Mixed_Weibull" but the software links to "2_Subpop-Mixed_Weibull," "3_Subpop-Mixed_Weibull" and "4_Subpop-Mixed_Weibull"|| Weibull++ ||Standard
|-
|Bayesian Weibull|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_B-W Configured as a "template" so the same content can be used in pages that linked separately for each type of Prior distribution. Still negotiating with developers on whether the links will be changed in the software for 8.0.5 and beyond.|| Weibull++ ||Standard
|-
|1P Exponential|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_1P-Exponential ||Weibull++ ||Standard
|-
|2P Exponential|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_2P-Exponential ||Weibull++ ||Standard
|-
|Lognormal|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Lognormal|| Weibull++ ||Standard
|-
|Normal|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Normal|| Weibull++ ||Standard
|-
|Generalized Gamma|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Generalized_Gamma|| Weibull++ ||Standard
|-
|Gamma ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Gamma|| Weibull++ ||Standard
|-
|Logistic|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Logistic|| Weibull++ ||Standard
|-
|Loglogistic|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Loglogistic|| Weibull++ ||Standard
|-
|Gumbel|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Gumbel|| Weibull++ ||Standard
|-
|CFM|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_CFM Configured as a "template" so the same content can be used in pages that linked separately for each distribution. Still negotiating with developers on whether the links will be changed in the software for 8.0.5 and beyond.|| Weibull++ ||Standard

|-
|Weibull Degradation|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWeibull_Degradation_Data|| Weibull++ ||Degradation

|-
|Actuarial-Simple||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_ActuarialSimple||Weibull++||Non-parametric LDA
|-
|Kaplan Meier||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_KaplanMeier||Weibull++||Non-parametric LDA
|-
|Actuarial-Standard||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Data_ActuarialStandard||Weibull++||Non-parametric LDA
|-
|Non-parametric LDA Plot|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_LDA_Plot|| Weibull++ ||Non-parametric LDA
|-
|Nevada folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Nevada|| Weibull++|| Warranty
|-
|Times-to-failure folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Weibull|| Weibull++ ||Warranty
|-
|Dates of failure folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_DateFailed|| Weibull++ ||Warranty
|-
|Usage folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BWarranty_Folio_Data_Usage|| Weibull++|| Warranty

|-
|Event Log Folio|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEvent_Log_Folio || Weibull++ || Event Log
|-
| Non-Parametric RDA Data || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BNon-Parametric_RDA_Data || Weibull++ || Non-parametric RDA

|-
|Parametric RDA Data || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BParameteric_RDA_Data || Weibull++ || Parametric RDA

|-
| Equation Fit Solver || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEquation_Fit_Solver_Data || Weibull++ || Equation Fit Solver
|-
| Equation Fit Solver Plot || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BEquation_Fit_Solver_Plot || Weibull++ || Equation Fit Solver
|-
| SimuMatic || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BSimuMatic_Data Configured as a "template" so the same content can be used in pages that were linked in 8.0.4 and below. || Weibull++|| SimuMatic

|-
|Target Reliability Estimator||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTarget_Reliability_Estimator||Weibull++||Target Reliability
|-
|General Spreadsheet|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio|| Weibull++|| Standard
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStandard_Folio_Plot|| Weibull++ || W++ Plot
|-
|Analysis Workbook || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BAnalysis_Workbook|| Weibull++|| Reports
|}

==Both Weibull++ and ALTA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Weibull++_ALTA http://reliawiki.org/index.php/Template:WebNotes/Weibull++_ALTA]
{|style="align:center" border="1"
|-
|Life Comparison||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BLife_Comparison||Weibull++ and ALTA||Life Comparison
|-
|Stress-Strength ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BStress-Strength||Weibull++ and ALTA||Stress-Strength
|-
|Test Design Folio||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_RDT||Weibull++ and ALTA||Test Design Folio
|-
|Test Design RDT Plot Table|| http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_RDT_PlotTable|| Weibull++ and ALTA ||Test Design Folio
|-
|Test Design Expected Failure Time||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_Expected_Failure_Time||Weibull++ and ALTA||Test Design Folio
|-
|Test Design Difference Detection Matrix||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BTest_Design_Difference_Detection_Matrix||Weibull++ and ALTA||Test Design Folio

|-
|Diagram ||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BDiagram||Weibull++ and ALTA||Diagram

|-
|Overlay Plot || http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BOverlay_Plot_None ||Weibull++ and ALTA ||Overlay Plot

|-
|Side by Side Plot||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BSide-By-Side_Plot|| Weibull++ and ALTA|| Side-by-Side Plot
|-
|-
|Maintenance Planning Tool||http://www.reliawiki.org/index.php/Template:WebNotes/Weibull%2B%2BMaintenance-Planning|| Weibull++ and ALTA|| Maintenance Planning Tool
|-
|}

==ALTA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://reliawiki.org/index.php/Template:WebNotes/ALTA http://reliawiki.org/index.php/Template:WebNotes/ALTA]
{|style="align:center" border="1"
|-
|General Spreadsheet || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio ||ALTA ||Standard Folio
|-
|Standard Folio Arrhenius || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_Arrhenius|| ALTA|| Standard Folio
|-
|Standard Folio Eyring || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_Eyring|| ALTA|| Standard Folio
|-
|Standard Folio Inverse Power Law|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_PowerLaw|| ALTA|| Standard Folio
|-
|Standard Folio Temperature Humidity || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_TempHumidity ||ALTA ||Standard Folio
|-
|Standard Folio Temperature Non-Thermal || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_TempNonThermal|| ALTA ||Standard Folio
|-
|Standard Folio Generalized Eyring|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_GenEyring|| ALTA|| Standard Folio
|-
|Standard Folio Proportional Hazards || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_PHazards|| ALTA|| Standard Folio
|-
|Standard Folio General Log-Linear|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_GenModel|| ALTA|| Standard Folio
|-
|Standard Folio Cumulative Damage|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Standard_Folio_Data_CumDamage|| ALTA|| Standard Folio

|-
|ALTA Degradation|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTAALTA_Degradation_Data|| ALTA|| Degradation

|-
|Stress Profile || http://www.reliawiki.org/index.php/Template:WebNotes/ALTAFolio|| ALTA ||Stress Profile
|-
|ALTA Test Plan || http://www.reliawiki.org/index.php/Template:WebNotes/ALTATest_Plan ||ALTA ||Test Plan
|-
|SimuMatic|| http://www.reliawiki.org/index.php/Template:WebNotes/ALTASimumatic_Data Configured as a "template" so the same content can be used in pages that were linked in 8.0.4 and below. ||ALTA ||SimuMatic

|-
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/ALTAStandard_Folio_Plot|| ALTA || ALTA Plot
|-
|}

==BlockSim==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/BlockSim http://www.reliawiki.com/index.php/Template:WebNotes/BlockSim]
{|style="align:center" border="1"
|-
|Allocation Analysis || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAllocation_Analysis_Folio|| BlockSim|| Allocation Analysis
|-
|Analytical FRED|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_FRED_Report|| BlockSim || FRED Report
|-
|Simulation FRED || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_FRED_Report|| BlockSim|| FRED Report
|-
|Analysis Workbook|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalysis_Workbook ||BlockSim || Analysis Workbook
|-
|Analytical RBD || http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_RBD_Diagram|| BlockSim ||Analytical RBD

|-
|Analytical Fault Tree|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimAnalytical_Fault_Tree_Diagram|| BlockSim ||Analytical Fault Tree
|-
|Simulation RBD|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_RBD_Diagram|| BlockSim ||Simulation RBD
|-
|Simulation Fault Tree|| http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimSimulation_Fault_Tree_Diagram|| BlockSim ||Simulation Fault Tree
|-
|Plot Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimPlot||BlockSim||Plot Sheet
|-
|Overlay Plot||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimOverlay_Plot_None||BlockSim||Overlay Plot
|-
|Expert Sheet||http://www.reliawiki.org/index.php/Template:WebNotes/BlockSimExpert_Sheet||BlockSim||Expert Sheet
|-
|}

==Xfmea==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/Xfmea http://www.reliawiki.com/index.php/Template:WebNotes/Xfmea] 

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaSystemTree || Xfmea || System Tree
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaProperties|| Xfmea|| Item Properties
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaFMRA||Xfmea|| FMRA
|-
|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDFR || Xfmea || DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaRisk_Discovery_Questions || Xfmea || Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaRisk_Discovery_Ratings|| Xfmea || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaAnalysis_Plan || Xfmea || Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaPFD||Xfmea|| PFD
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaFMEA ||Xfmea|| FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDRBFM || Xfmea || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaDVPR||Xfmea|| DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/XfmeaControl_Plan||Xfmea|| Control Plan
|-

|}

==RCM++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release. The old pages will remain on the server (set up to display the same content from the new template) until users have a chance to upgrade to Version 9.

[http://www.reliawiki.com/index.php/RCM http://www.reliawiki.com/index.php/Template:WebNotes/RCM]

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++SystemTree || RCM++|| System Tree
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Properties|| RCM++ || Item Properties
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++FMRA|| RCM++ || FMRA
|-
|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DFR || RCM++|| DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Risk_Discovery_Questions || RCM++|| Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Risk_Discovery_Ratings|| RCM++ || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Analysis_Plan || RCM++|| Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++PFD|| RCM++ || PFD
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++FMEA || RCM++ || FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DRBFM || RCM++ || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++DVPR|| RCM++ || DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/RCM++Control_Plan|| RCM++ || Control Plan

|-

|}

==RBI==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/RBI http://www.reliawiki.com/index.php/Template:WebNotes/RBI]

{|style="align:center" border="1"
|System Tree || http://www.reliawiki.org/index.php/Template:WebNotes/RBISystemTree || RBI || System Tree
|-
|FMRA ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIFMRA|| RBI || FMRA
|-
|Item Properties||http://www.reliawiki.org/index.php/Template:WebNotes/RBIProperties|| RBI || Item Properties
|-
|RBI General Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIGeneral_Properties || RBI || General Properties
|-
|RBI Damage Factors Selection ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDamage_Factors_Selection || RBI || Damage Factors Selection
|-
|RBI Damage Factor Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDamage_Factor_Properties || RBI || Damage Factor Properties
|-
|RBI Consequence Properties ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIConsequence_Properties || RBI || Consequence Properties
|-
|RBI Results ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIResults || RBI || Results
|-
|RBI HexTubes ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIHexTube_Properties || RBI || HexTube properties
|-
|RBI Pressure Relief Devices||http://www.reliawiki.org/index.php/Template:WebNotes/RBIPressureRelief_Properties || RBI || Pressure Relief Devices
|-

|DFR Planner || http://www.reliawiki.org/index.php/Template:WebNotes/RBIDFR || RBI || DFR Planner
|-
|Risk Discovery Questions ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIRisk_Discovery_Questions || RBI || Risk Discovery Questions
|-
|Risk Discovery Ratings||http://www.reliawiki.org/index.php/Template:WebNotes/RBIRisk_Discovery_Ratings|| RBI || Risk Discovery Ratings
|-
|Analysis Plan || http://www.reliawiki.org/index.php/Template:WebNotes/RBIAnalysis_Plan || RBI || Analysis Plan
|-
|PFD Worksheet||http://www.reliawiki.org/index.php/Template:WebNotes/RBIPFD|| RBI || PFD Worksheet
|-
|FMEA ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIFMEA || RBI || FMEA
|-
|DRBFM ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDRBFM || RBI || DRBFM
|-
|DVP&R ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIDVPR|| RBI || DVP&R
|-
|Control Plan ||http://www.reliawiki.org/index.php/Template:WebNotes/RBIControl_Plan|| RBI || Control Plan
|-
|RBI Plots ||http://www.reliawiki.org/index.php/Template:WebNotes/RBI_Plot|| RBI || RBI Plots (V10 only)
|-
|}

==RGA==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/RGA http://www.reliawiki.com/index.php/Template:WebNotes/RGA]

{|style="align:center" border="1"
| General Spreadsheet||http://www.reliawiki.org/index.php/Template:WebNotes/RGAGeneral_Spreadsheet||RGA||Standard
|-
| Duane Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGADuane||RGA||Standard
|-
| Crow-AMSAA Model for Developmental Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_AMSAA_Developmental||RGA||Standard
|-
| Crow-AMSAA Model for Fleet Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_AMSAA_Fleet||RGA||Standard
|-
| Crow Extended Model for Developmental Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Developmental||RGA||Standard
|-
| Crow Extended Model for Repairable Systems Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Repairable||RGA||Standard
|-
| Crow Extended Model for Fleet Data||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Fleet||RGA||Standard
|-
| Crow Extended-Continuous Evaluation Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGACrow_Extended_Continuous||RGA||Standard
|-
| Lloyd-Lipow Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGALloyd-Lipow||RGA||Standard
|-
| Standard Gompertz Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAStandard_Gompertz||RGA||Standard
|-
| Modified Gompertz Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAModified_Gompertz||RGA||Standard
|-
| Logistic Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGALogistic||RGA||Standard
|-
| Power Law Model||http://www.reliawiki.org/index.php/Template:WebNotes/RGAPower_Law||RGA||Standard

|-
| Multi-Phase Plots||http://www.reliawiki.org/index.php/Template:WebNotes/RGAMultiPhase_Plot||RGA||Multi-Phase
|-
| Growth Planning Folio||http://www.reliawiki.org/index.php/Template:WebNotes/RGAGrowth_Planning||RGA||Growth Planning
|-
| Mission Profile Folio||http://www.reliawiki.org/index.php/Template:WebNotes/RGAMission_Profile||RGA||Mission Profile
|-
| RGA SimuMatic||http://www.reliawiki.org/index.php/Template:WebNotes/RGASimuMatic||RGA||SimuMatic
|-
| Repairable Systems Reliability Demonstration Tests||http://www.reliawiki.org/index.php/Template:WebNotes/RGARepairable_RDT||RGA||RDT

|-
| Plot Sheets in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAPlot||RGA||Plot Sheet
|-
| Overlay Plots in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAOverlay_Plot_None||RGA||Overlay
|-
| Side-by-Side Plots in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGASide-By-Side_Plot||RGA||Side-by-Side
|-
| Analysis Workbooks in RGA||http://www.reliawiki.org/index.php/Template:WebNotes/RGAAnalysis_Workbook||RGA||Analysis Workbook
|-
|}

==DOE++==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.com/index.php/Template:WebNotes/DOE http://www.reliawiki.com/index.php/Template:WebNotes/DOE]

{|style="align:center" border="1"
| Two Level Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOETwo_Level_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Plackett-Burman Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEPlackett_Burman_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| General Full Factorial Design||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGeneral_Full_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Taguchi OA Factorial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOETaguchi_OA_Factorial||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Central Composite Response Surface Method (RSM) Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOECentral_Composite_RSM||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Box-Behnken Response Surface Method (RSM) Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEBox_Behnken_RSM||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| One Factor Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOne_Factor||Standard Design Folios (and Robust when type is selected on Design tab)
|-
| Simplex Lattice Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimplex_Lattice||Mixture Design Folios
|-
| Simplex Centroid Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimplex_Centroid||Mixture Design Folios
|-
| Simplex Axial Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOESimpex_Axial||Mixture Design Folios
|-
| Extreme Vertex Designs||http://www.reliawiki.org/index.php/Template:WebNotes/DOEExtreme_Vertex||Mixture Design Folios
|-
| Robust Design Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOERobust_Data||Robust Design Folios -- show in all tabs except "Design"
|-
| Free Form Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEFree_Form_Design||Free Form Folio
|-
| Multiple Linear Regression Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEMultiple_Linear_Regression||Multiple Linear Regression Folio
|-
| One-Way ANOVA Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEANOVA||One-Way Anova Folio
|-
| Linearity & Bias Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOELinearity_and_Bias||Linearity & Bias Folio
|-
| Gage Agreement Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGage_Agreement||Gage Agreement Folio
|-
| Gage R&R Folios||http://www.reliawiki.org/index.php/Template:WebNotes/DOEGage_R||Gage R&R Folio
|-
| Optimal Solution Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Optimal_Solution_Plot||Optimization Folio
|-
| Overlaid Contour Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Overlaid_Contour_Plot||Optimization Folio
|-
| Dynamic Overlaid Contour Plots||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOptimization_Dynamic_Overlaid_Contour_Plot||Optimization Folio
|-
| Plot Sheets in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOEPlot||Plot Sheet
|-
| Overlay Plots in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOEOverlay_Plot_None||Overlay Plot
|-
| Side-by-Side Plots in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOESide_By_Side_Plot||Side-by-Side Plot
|-
| Spreadsheets in DOE++||http://www.reliawiki.org/index.php/Template:WebNotes/DOESpreadsheet||Spreadsheet
|-
| Simulation Worksheets||http://www.reliawiki.org/index.php/Template:WebNotes/DOEExpert_Sheet||Simulation Worksheet
|-
|}

==RENO==
[http://reliawiki.org/index.php/Template:WebNotes/RENO http://reliawiki.org/index.php/Template:WebNotes/RENO]

'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

{|style="align:center" border="1"
|-
| RENO Flowcharts||http://www.reliawiki.org/index.php/Template:WebNotes/RENORENO_Flowchart_Flowchart||Flowchart
|-
| RENO Plot Sheets||http://www.reliawiki.org/index.php/Template:WebNotes/RENOPlot||Flowchart Plot Sheet
|-
|}

==Lambda Predict==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://reliawiki.org/index.php/Template:WebNotes/Lambda_Predict http://reliawiki.org/index.php/Template:WebNotes/Lambda_Predict]
{|style="align:center" border="1"
|-
|Generic ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictPrediction||Prediction Window - Blank hierarchy or Generic branch selected
|-
|MIL-217 Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictMIL-217||Prediction Window - MIL-217 Branch Selected
|-
| Bellcore/Telcordia Predictions||http://www.reliawiki.org/index.php/Template:WebNotes/PredictTelcordia||Prediction Window - Bellcore/Telcordia Branch Selected
|-
| NSWC (Mechanical) Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictNSWC||Prediction Window - NSWC Branch Selected
|-
| FIDES Predictions ||http://www.reliawiki.org/index.php/Template:WebNotes/PredictFIDES||Prediction Window - FIDES Branch Selected
|-
| Derating||http://www.reliawiki.org/index.php/Template:WebNotes/PredictDerating||Select Derating Standard or Manage Derating Standard
|-
| Equal Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Equal||Allocation
|-
| AGREE Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_AGREE||Allocation
|-
| Feasibility of Objectives Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Feasibility||Allocation
|-
| ARINC Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_ARINC||Allocation
|-
| Repairable Allocation||http://www.reliawiki.org/index.php/Template:WebNotes/PredictAllocation_Repairable||Allocation
|-
| Plots in Lambda Predict||http://www.reliawiki.org/index.php/Template:WebNotes/PredictPlot||Plot Viewer
|-
| Import BOM||http://www.reliawiki.org/index.php/Template:WebNotes/PredictImport_BOM||Import BOM Wizard or Import Templates Window
|}

==MPC==
'''UPDATE - May 2013''' These pages were moved to the Template namespace prior to Version 9 release.

[http://www.reliawiki.org/index.php/Template:WebNotes/MPC http://www.reliawiki.org/index.php/Template:WebNotes/MPC]

{|style="align:center" border="1"
| System Hierarchy and MSI Selection||http://www.reliawiki.org/index.php/Template:WebNotes/MPCSystemHierarchy||System Hierarchy
|-
| F-F-E-C||http://www.reliawiki.org/index.php/Template:WebNotes/MPCFMEA||F-F-E-C
|-
| Structural Hierarchy and SSI Selection||http://www.reliawiki.org/index.php/Template:WebNotes/MPCStructuralHierarchy||Structural Hierarchy
|-
| Accidental Damage Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCAccidentalDamage||Accidental Damage Analysis (includes both Metals and Non-Metals)
|-
| Environmental Deterioration Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCEnvironmental_Deterioration||Environmental Deterioration Analysis
|-
| Zonal Hierarchy and Selecting Items for Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalHierarchy||Zonal Hierarchy
|-
| Standard Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalStandard||Standard Zonal Analysis
|-
| Enhanced Zonal Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalEnhanced||Enhanced Zonal Analysis
|-
| L/HIRF Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCZonalLHIRF||Zonal L/HIRF Analysis
|-
| Fatigue Damage Analysis||http://www.reliawiki.org/index.php/Template:WebNotes/MPCFatigue_Damage||Fatigue Damage Analysis (V10 only)
|-

|}

==Retired Plot Type Descriptions Used in Version 8==
The following pages were used in Version 8 when the user selected a different plot type. In Version 9, the description will be directly available from an (i) icon in the plot control panel, so these pages are no longer needed.

{|style="align:center" border="1"
|-
|Contour Plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptContour|| Weibull++ || W++ Plot
|-
|Probability Weibull Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptProbability|| Weibull++ ||W++ Plot
|-
|Reliability vs. Time Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptReliability|| Weibull++ ||W++ Plot
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptUnreliability|| Weibull++ ||W++ Plot
|-
|pdf Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptPdf|| Weibull++ ||W++ Plot
|-
|Failure Rate vs. Time|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFailureRate|| Weibull++ ||W++ Plot
|-
|F/S Histogram|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSHistogram|| Weibull++ ||W++ Plot
|-
|F/S Pie|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSPie|| Weibull++ ||W++ Plot
|-
|F/S Timeline|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Standard_Folio_Plot_ptFSTimeline|| Weibull++ ||W++ Plot
|-
|Degradation vs. time(linear) plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Weibull_Degradation_Plot_ptDegradationLinear|| Weibull++ ||Degradation
|-
|Degradation vs. time(log) plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Weibull_Degradation_Plot_ptDegradationLog|| Weibull++ ||Degradation
|-
|-
|Chi-Squared-Sales||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptChiSqSales||Weibull++||Warranty
|-
|Chi-Squared Returns||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptChiSqReturns||Weibull++||Warranty

|-
|Expected Failures||http://www.reliawiki.org/index.php/Weibull%2B%2B_Warranty_Folio_Plot_ptExpectedFailures|| Weibull++||Warranty
|-
|Overlay Plot Probability ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptProbability ||Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Reliability vs. Time|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptReliability|| Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Unreliability vs. Time || http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptUnreliability|| Weibull++ and ALTA|| Overlay Plot
|-
|Overlay Plot Pdf Plot|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptPdf ||Weibull++ and ALTA ||Overlay Plot
|-
|Overlay Plot Failure Rate vs. Time ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptFailureRate|| Weibull++ and ALTA|| Overlay Plot
|-
|Overlay Plot Contour Plot || http://www.reliawiki.org/index.php/Weibull%2B%2B_Overlay_Plot_ptContour ||Weibull++ and ALTA|| Overlay Plot
|-
| Non-parametric RDA folios (plot) ||http://www.reliawiki.org/index.php/Weibull%2B%2B_Non-Parametric_RDA_Plot ||Weibull++ || Non-parametric RDA
|-
|Parametric RDA Plots|| http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot || Weibull++ || Parametric RDA
|-
|Parametric Cum. Number of Failures Plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CumNumFailures||Weibull++||Parametric RDA
|-
|Cum. Failure Intensity vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CumFI||Weibull++||Parametric RDA
|-
|Instant. Failure Intensity vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_InstFI||Weibull++||Parametric RDA
|-
|Cond. Reliability vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CondReliability||Weibull++||Parametric RDA
|-
|Cond. Unreliability vs. Time||http://www.reliawiki.org/index.php/Weibull%2B%2B_Parameteric_RDA_Plot_CondUnreliability||Weibull++||Parametric RDA
|-
| Simumatic Plot || http://www.reliawiki.org/index.php/Weibull++_Simumatic_Plot || Weibull++ || SimuMatic
|-
|Diagram Reliability plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptReliability||Weibull++ and ALTA||Diagram
|-
|Diagram Unreliability plot||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptUnreliability||Weibull++ and ALTA||Diagram
|-
|Diagram Pdf||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptPdf ||Weibull++ and ALTA||Diagram
|-
|Diagram Failure Rate||http://www.reliawiki.org/index.php/Weibull%2B%2B_Diagram_Plot_ptFailureRate ||Weibull++ and ALTA||Diagram
|-
|Use Level Probability Weibull|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptUseLevel|| ALTA|| ALTA Plots
|-
|Reliability vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptReliability|| ALTA|| ALTA Plots
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptUnreliability|| ALTA|| ALTA Plots
|-
|Pdf Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptPdf|| ALTA|| ALTA Plots
|-
|Failure Rate vs. Time Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptFailureRate|| ALTA|| ALTA Plots
|-
|Life vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptLifeStress|| ALTA|| ALTA Plots
|-
|STD vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStdDevStress|| ALTA|| ALTA Plots
|-
|AF vs. stress Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptAFStress|| ALTA|| ALTA Plots
|-
|Cox-Snell Residual Plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Standard_Folio_Plot_ptCoxSnellResiduals|| ALTA|| ALTA Plots
|-
|Probability Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptProbability|| ALTA|| ALTA Plots
|-
|Standardized Residuals Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStandardResiduals|| ALTA|| ALTA Plots
|-
|Standardized vs. Fitted Plot|| http://www.reliawiki.com/index.php/ALTA_ALTA_Standard_Folio_Plot_ptStandardFitted|| ALTA|| ALTA Plots
|-
|Degradation vs. time(linear) plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Degradation_Plot_ptDegradationLinear|| ALTA|| Degradation
|-
|Degradation vs. time(log) plot|| http://www.reliawiki.org/index.php/ALTA_ALTA_Degradation_Plot_ptDegradationLog|| ALTA|| Degradation
|-
|ALTA Simumatic Plot ||http://www.reliawiki.org/index.php/ALTA_Simumatic_Plot ||ALTA ||SimuMatic
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptUnreliability The analytical RBD plot notes were configured as "templates" so the same content can be used in the equivalent analytical fault tree plot pages that were linked in 8.0.4 and below.|| BlockSim|| Analytical RBD Plots
|-
|Reliability vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptReliability|| BlockSim ||Analytical RBD Plots
|-
|Pdf Plot ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptPdf|| BlockSim ||Analytical RBD Plots
|-
|Failure vs. Time plot ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptFailureRate|| BlockSim ||Analytical RBD Plots
|-
|RI vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptDynamicRI|| BlockSim ||Analytical RBD Plots
|-
|Static RI ||http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptStaticRI|| BlockSim ||Analytical RBD Plots
|-
|Static RI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptTableauRI|| BlockSim ||Analytical RBD Plots
|-
|Block Unreliability|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockUnreliability|| BlockSim ||Analytical RBD Plots
|-
|Block Reliability|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockReliability|| BlockSim ||Analytical RBD Plots
|-
|Block pdf|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockPdf|| BlockSim ||Analytical RBD Plots
|-
|Block Failure Rate|| http://www.reliawiki.org/index.php/BlockSim_Analytical_RBD_Plot_ptAnBlockFailureRate|| BlockSim ||Analytical RBD Plots
|-
|RS FCI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSFCIBarChart The simulation RBD plot notes were configured as "templates" so the same content can be used in the equivalent simulation fault tree, FMRA and phase diagram plot pages that were linked in 8.0.4 and below.|| BlockSim ||Simulation RBD Plots
|-
|Point Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPointAvailability|| BlockSim ||Simulation RBD Plots
|-
|Point Reliability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPointReliability|| BlockSim ||Simulation RBD Plots
|-
|Point both A & R|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBothPointAR|| BlockSim ||Simulation RBD Plots
|-
|Cost|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCost|| BlockSim ||Simulation RBD Plots
|-
|Mean Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptMeanAvailability|| BlockSim ||Simulation RBD Plots
|-
|Point System Failures|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptSysFailures|| BlockSim ||Simulation RBD Plots
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptThroughput|| BlockSim ||Simulation RBD Plots
|-
|System Up/Down|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptSystemUpDown|| BlockSim ||Simulation RBD Plots
|-
|Block Up/Down|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockUpDown|| BlockSim ||Simulation RBD Plots
|-
|RS FCI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSFCITableau|| BlockSim ||Simulation RBD Plots
|-
|RS DECI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDECIBarChart|| BlockSim ||Simulation RBD Plots
|-
|RS DECI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDECITableau|| BlockSim ||Simulation RBD Plots
|-
|RS DTCI|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDTCIBarChart|| BlockSim ||Simulation RBD Plots
|-
|RS DTCI Tableau|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptRSDTCITableau|| BlockSim ||Simulation RBD Plots
|-
|Block Availability|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockAvailability|| BlockSim ||Simulation RBD Plots
|-
|Block Costs|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockCosts|| BlockSim ||Simulation RBD Plots
|-
|Block Downtime|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockDownTime|| BlockSim ||Simulation RBD Plots
|-
|Block Expected Failures|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExpectedFailures|| BlockSim ||Simulation RBD Plots
|-
|Expected Downing Events|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExpectedEvents|| BlockSim ||Simulation RBD Plots
|-
|Block ThroughPut|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockThroughPut|| BlockSim|| Simulation RBD Plots
|-
|Excess Capacity|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockExcessCapacity|| BlockSim ||Simulation RBD Plots
|-
|Block Backlog|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockBackLog|| BlockSim ||Simulation RBD Plots
|-
|Backlog Processed|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockBackLogProcessed|| BlockSim ||Simulation RBD Plots
|-
|Block Results Bubble|| http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptBlockResultsBubble|| BlockSim ||Simulation RBD Plots
|-

|Simulation RBD Plot Crew Accepted Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewAcceptedCalls ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Rejected Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewRejectedCalls|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Costs || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewCrewCosts ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Crew Time Used || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptCrewTimeUsed ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Average Stock Level || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolAverageStockLevel ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Items Dispensed || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolItemsDispensed|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Average Time To Dispense || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolAverageTimeToDispense|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Rejected Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolRejectedCalls|| BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Emergency Calls || http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolEmergingCalls|| BlockSim ||Simulation RBD Plots
|-
|Simulation RBD Plot Pool Costs ||http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolCosts ||BlockSim|| Simulation RBD Plots
|-
|Simulation RBD Plot Pool Cost Per Item ||http://www.reliawiki.org/index.php/BlockSim_Simulation_RBD_Plot_ptPoolCostPerItem|| BlockSim ||Simulation RBD Plots
|-
|Simulation Fault Tree Diagram||http://www.reliawiki.org/index.php/BlockSim_Simulation_Fault_Tree_Diagram||BlockSim||Simulation Fault Tree
|-
|Phase Diagram|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Diagram|| BlockSim ||Phase Diagram
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemThroughPut ||BlockSim ||Phase Diagram Plots (Unique)
|-
|Expected Events|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemExpectedEvents ||BlockSim ||Phase Diagram Plots (Unique)
|-
|System Expected Failures|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemExpectedFailures|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Downtime|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemDownTime|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Costs|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemCosts|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Availability|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemAvailability|| BlockSim ||Phase Diagram Plots (Unique)
|-
|System Availability-All Events|| http://www.reliawiki.org/index.php/BlockSim_Phase_Diagram_Plot_ptSystemAvailability_AllEvents|| BlockSim ||Phase Diagram Plots (Unique)
|-
|Unreliability vs. Time Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptUnreliability|| BlockSim ||Overlay Plot Analytical
|-
|Reliability vs. Time plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptReliability|| BlockSim|| Overlay Plot Analytical
|-
|Pdf Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPdf|| BlockSim ||Overlay Plot Analytical
|-
|Failure Rate vs. Time|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptFailureRate|| BlockSim ||Overlay Plot Analytical
|-
|Point Availability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPointAvailability|| BlockSim ||Overlay Plot Simulation
|-
|Point Reliability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptPointReliability|| BlockSim ||Overlay Plot Simulation
|-
|Cost|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptCost|| BlockSim ||Overlay Plot Simulation
|-
|Mean Availability|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptMeanAvailability|| BlockSim ||Overlay Plot Simulation
|-
|System Failures|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptSysFailures|| BlockSim ||Overlay Plot Simulation
|-
|Throughput|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptThroughput|| BlockSim ||Overlay Plot Simulation
|-
|System Bubble Plot|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptSystemResultsBubble|| BlockSim ||Overlay Plot Simulation

|-
|Overlay Plot || http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot|| BlockSim|| Overlay Plot

|-
|Overlay Plot Reliability vs. Time (for mixed diagrams)|| http://www.reliawiki.org/index.php/BlockSim_Overlay_Plot_ptMixedMultiplotReliability|| BlockSim ||Overlay Plot
|}

[[Category: List of Webnotes Pages]]

Template:WebNotes/DOEExtreme Vertex

2015-02-24T21:41:01Z

Chris Kahn: Created page with '{{Template:NoSkin}} {{Template: Web Notes DOE Banner}} |{{Font|Extreme Vertex Designs|11|tahoma|bold|gray}} Extreme vertex designs are used when both lower and upper bound constr…'

{{Template:NoSkin}}
{{Template: Web Notes DOE Banner}}
|{{Font|Extreme Vertex Designs|11|tahoma|bold|gray}}
Extreme vertex designs are used when both lower and upper bound constraints on the components are used, or when linear constraints are added to several components. These constraints define the feasible region of the experiment, which is usually not a simplex. All the vertices of the feasible region will be included in the experiment.

|}
{{Font|Learn more from...|11|tahoma|bold|gray}}
{| border="0" align="left" cellpadding="0" cellspacing="3"
|-
| [[Image:Helpblue.png]]
| [http://help.synthesisplatform.net/doex/extreme_vertex_designs.htm the help file...]
|-
| [[Image:Book blue.png]]
| [http://www.reliawiki.org/index.php/Mixture_Design the theory textbook...]
|}

 
 
 
 
 
 
 
 
 
 

[[File:docedit.png|20px|right|link=http://www.reliawiki.org/index.php?title=Template:WebNotes/DOEExtreme_Vertex&action=edit]]

Template:WebNotes/DOESimplex Axial

2015-02-24T21:39:18Z

Chris Kahn: Created page with '{{Template:NoSkin}} {{Template: Web Notes DOE Banner}} |{{Font|Simplex Axial Designs|11|tahoma|bold|gray}} Simplex axial design is usually used in a screening experiment where fi…'

{{Template:NoSkin}}
{{Template: Web Notes DOE Banner}}
|{{Font|Simplex Axial Designs|11|tahoma|bold|gray}}
Simplex axial design is usually used in a screening experiment where first degree models are to be fitted. Most of the runs in a simplex axial design are inside the simplex, and all the runs are on the axial of each component, which is the imaginary vertical line extending from the base point to the vertex of that component.

|}
{{Font|Learn more from...|11|tahoma|bold|gray}}
{| border="0" align="left" cellpadding="0" cellspacing="3"
|-
| [[Image:Helpblue.png]]
| [http://help.synthesisplatform.net/doex/simplex_designs.htm the help file...]
|-
| [[Image:Book blue.png]]
| [http://www.reliawiki.org/index.php/Mixture_Design the theory textbook...]
|}

 
 
 
 
 
 
 
 
 
 

[[File:docedit.png|20px|right|link=http://www.reliawiki.org/index.php?title=Template:WebNotes/DOESimplex_Axial&action=edit]]

Template:WebNotes/DOESimplex Centroid

2015-02-24T21:38:35Z

Chris Kahn:

{{Template:NoSkin}}
{{Template: Web Notes DOE Banner}}
|{{Font|Simplex Centroid Designs|11|tahoma|bold|gray}}
A simplex centroid design only includes the centroid points. Therefore, in any given run, the values of all non-zero components are the same. For a design with a degree of centroid of ''m'', centroids of spaces up to ''m'' dimensions are added in the experiment. The center of a face is the centroid of a 2-dimensional space.

|}
{{Font|Learn more from...|11|tahoma|bold|gray}}
{| border="0" align="left" cellpadding="0" cellspacing="3"
|-
| [[Image:Helpblue.png]]
| [http://help.synthesisplatform.net/doex/simplex_designs.htm the help file...]
|-
| [[Image:Book blue.png]]
| [http://www.reliawiki.org/index.php/Mixture_Design the theory textbook...]
|}

 
 
 
 
 
 
 
 
 
 

[[File:docedit.png|20px|right|link=http://www.reliawiki.org/index.php?title=Template:WebNotes/DOESimplex_Centroid&action=edit]]

Template:WebNotes/DOESimplex Centroid

2015-02-24T21:37:42Z

Chris Kahn: Created page with '{{Template:NoSkin}} {{Template: Web Notes DOE Banner}} |{{Font|Simplex Centroid Designs|11|tahoma|bold|gray}} A simplex centroid design only includes the centroid points. Therefo…'

Template:WebNotes/DOESimplex Lattice

2015-02-24T21:37:01Z

Chris Kahn:

{{Template:NoSkin}}
{{Template: Web Notes DOE Banner}}
|{{Font|Simplex Lattice Designs|11|tahoma|bold|gray}}
A {''q'', ''m''} simplex lattice design has ''q'' components, and each component can take ''m''+1 equally spaced values from 0 to 1. m is the called the ''degree of the design''. More runs will be included in designs with higher degree values, and the obtained data can be used to fit a higher order polynomial model.

|}
{{Font|Learn more from...|11|tahoma|bold|gray}}
{| border="0" align="left" cellpadding="0" cellspacing="3"
|-
| [[Image:Helpblue.png]]
| [http://help.synthesisplatform.net/doex/simplex_designs.htm the help file...]
|-
| [[Image:Book blue.png]]
| [http://www.reliawiki.org/index.php/Mixture_Design the theory textbook...]
|}

 
 
 
 
 
 
 
 
 
 

[[File:docedit.png|20px|right|link=http://www.reliawiki.org/index.php?title=Template:WebNotes/DOESimplex_Lattice&action=edit]]

Template:WebNotes/DOESimplex Lattice

2015-02-24T21:34:49Z

Chris Kahn: Created page with '{{Template:NoSkin}} {{Template: Web Notes DOE Banner}} |{{Font|Simplex Lattice Designs|11|tahoma|bold|gray}} A {''q'', ''m''} simplex lattice design has ''q'' components, and eac…'

ReliaSoft API Reference

2014-10-15T20:59:33Z

Chris Kahn: /* Application Examples */

{{Template:API|Version 9}}

The Synthesis API can be used to accomplish many of the same tasks as within Synthesis applications, and it also enables seamless integration of the Synthesis Platform with other systems within your organization—all through a programmer's own custom-developed code. This allows you to create customizable and automated solutions to reliability engineering problems by integrating Synthesis functionality into other applications.

This reference describes all of the programming elements in the API. The sample code and documentation have been prepared for the Visual Basic and .NET development environments, and it is assumed that the reader is familiar with them.

== Requirements ==

Before using the Synthesis API, note the following requirements:

*Your code must include a reference to the ReliaSoft Synthesis API Library. The library is located in the folder where ReliaSoft Synthesis is installed. By default, this folder is "C:\Program Files\ReliaSoft\Synthesis 9."
** .NET developers – use the SynthesisAPI.dll library
** VB6 / VBA developers – use the SynthesisAPI.tlb library

*The version of the Synthesis Platform that you've installed (32- vs. 64-bit) must match your installed version of Microsoft Office. If they do not match, you may see an [http://www.reliasoft.com/support/rs20024.htm error] related to ActiveX controls.

== API Elements ==

The Synthesis API includes a rich set of programming elements that allow you to work with any of the following components of the Synthesis Platform:

*'''[[Repository Class|Repositories]]''': {{Template:Repository Class.Cmt}}
*'''[[WeibullDataSet Class|Weibull++ Standard Folio]]''': {{Template:WeibullDataSet Class.Cmt}}
*'''[[ALTADataSet Class|ALTA Standard Folio]]''': {{Template:ALTADataSet Class.Cmt}}
*'''[[WAPlots Class|Plots in Weibull++/ALTA]]''': {{Template:WAPlots Class.Cmt}}
*'''[[Resource Classes|Resources]]''': {{Template:Resource Classes.Cmt}}
*'''[[Common Class|Displayed Language]]''': {{Template:Common Class.Cmt}}

A complete list of all the classes and enumerations in the Synthesis API is available [[Full Synthesis API|here]].

== Application Examples ==

'''Excel VBA Samples'''

Use the following links to download macro-enabled Excel files (*.xlsm) that utilize the Synthesis API. Note that to run/view the underlying code, the [http://msdn.microsoft.com/en-us/library/bb608625.aspx Developer tab must be enabled] in Excel so you can enter the Visual Basic for Applications (VBA) environment by choosing '''Developer > View Code'''. Also, you must have [http://office.microsoft.com/en-us/excel-help/enable-or-disable-macros-in-office-documents-HA010031071.aspx macros enabled] to run the example files. If Excel displays a warning regarding macros in these files, select to enable them.
*Use Synthesis analysis engines in Excel
** [http://www.reliasoft.com/synthesis/api/examples/WeibullExample.xlsm Life Data Analysis in Excel (237 KB)] ([[Life Data Analysis in Microsoft Excel - Explanation|Code explanation]])
** [http://www.reliasoft.com/synthesis/api/examples/ALTAExample.xlsm Accelerated Life Testing Analysis (ALTA) in Excel (221 KB)] ([[Accelerated Life Testing Analysis in Microsoft Excel - Explanation|Code explanation]])
* Transfer data from Excel to the Synthesis Reliability Data Warehouse (RDW)
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Standard.xlsm Excel to Standard Repository (2.64 MB)]
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Enterprise.xlsm Excel to Enterprise SQL Repository (2.65 MB)] ''Requires code modification to reference a SQL repository.''
* Use Excel to update Universal Reliability Definitions (URDs) used in BlockSim, etc.
** [http://www.reliasoft.com/synthesis/api/examples/URDExample.xlsm Update URDs with Excel (108 KB)]

ReliaSoft API Reference

2014-10-15T20:58:03Z

Chris Kahn: /* Application Examples */

{{Template:API|Version 9}}

The Synthesis API can be used to accomplish many of the same tasks as within Synthesis applications, and it also enables seamless integration of the Synthesis Platform with other systems within your organization—all through a programmer's own custom-developed code. This allows you to create customizable and automated solutions to reliability engineering problems by integrating Synthesis functionality into other applications.

This reference describes all of the programming elements in the API. The sample code and documentation have been prepared for the Visual Basic and .NET development environments, and it is assumed that the reader is familiar with them.

== Requirements ==

Before using the Synthesis API, note the following requirements:

*Your code must include a reference to the ReliaSoft Synthesis API Library. The library is located in the folder where ReliaSoft Synthesis is installed. By default, this folder is "C:\Program Files\ReliaSoft\Synthesis 9."
** .NET developers – use the SynthesisAPI.dll library
** VB6 / VBA developers – use the SynthesisAPI.tlb library

*The version of the Synthesis Platform that you've installed (32- vs. 64-bit) must match your installed version of Microsoft Office. If they do not match, you may see an [http://www.reliasoft.com/support/rs20024.htm error] related to ActiveX controls.

== API Elements ==

The Synthesis API includes a rich set of programming elements that allow you to work with any of the following components of the Synthesis Platform:

*'''[[Repository Class|Repositories]]''': {{Template:Repository Class.Cmt}}
*'''[[WeibullDataSet Class|Weibull++ Standard Folio]]''': {{Template:WeibullDataSet Class.Cmt}}
*'''[[ALTADataSet Class|ALTA Standard Folio]]''': {{Template:ALTADataSet Class.Cmt}}
*'''[[WAPlots Class|Plots in Weibull++/ALTA]]''': {{Template:WAPlots Class.Cmt}}
*'''[[Resource Classes|Resources]]''': {{Template:Resource Classes.Cmt}}
*'''[[Common Class|Displayed Language]]''': {{Template:Common Class.Cmt}}

A complete list of all the classes and enumerations in the Synthesis API is available [[Full Synthesis API|here]].

== Application Examples ==

'''Excel VBA Samples'''

Use the following links to download macro-enabled Excel files (*.xlsm) that utilize the Synthesis API. Note that to run/view the underlying code, the [http://msdn.microsoft.com/en-us/library/bb608625.aspx Developer tab must be enabled] in Excel so you can enter the Visual Basic for Applications (VBA) environment by choosing '''Developer > View Code'''. Also, you must have [http://office.microsoft.com/en-us/excel-help/enable-or-disable-macros-in-office-documents-HA010031071.aspx macros enabled] to run the example files. If Excel displays a warning regarding macros in these files, select to enable them.
*Use Synthesis analysis engines in Excel
** [http://www.reliasoft.com/synthesis/api/examples/WeibullExample.xlsm Life Data Analysis in Excel (237 KB)] ([[Life Data Analysis in Microsoft Excel - Explanation|Code explanation]])
** [http://www.reliasoft.com/synthesis/api/examples/ALTAExample.xlsm Accelerated Life Testing Analysis (ALTA) in Excel (221 KB)] ([[Accelerated Life Testing Analysis in Microsoft Excel - Explanation|Code explanation]])
* Transfer data from Excel to the Synthesis Reliability Data Warehouse (RDW)
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Standard.xlsm Excel to Standard Repository (2.64 MB)]
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Enterprise.xlsm Excel to Enterprise SQL Repository (2.65 MB)] ''Requires code modification to reference a SQL repository.''
* Use Excel to update Universal Reliability Definitions (URDs) for use in BlockSim, etc.
** [http://www.reliasoft.com/synthesis/api/examples/URDExample.xlsm Update URDs with Excel (108 KB)]

ReliaSoft API Reference

2014-10-15T20:56:07Z

Chris Kahn: /* Application Examples */

{{Template:API|Version 9}}

The Synthesis API can be used to accomplish many of the same tasks as within Synthesis applications, and it also enables seamless integration of the Synthesis Platform with other systems within your organization—all through a programmer's own custom-developed code. This allows you to create customizable and automated solutions to reliability engineering problems by integrating Synthesis functionality into other applications.

This reference describes all of the programming elements in the API. The sample code and documentation have been prepared for the Visual Basic and .NET development environments, and it is assumed that the reader is familiar with them.

== Requirements ==

Before using the Synthesis API, note the following requirements:

*Your code must include a reference to the ReliaSoft Synthesis API Library. The library is located in the folder where ReliaSoft Synthesis is installed. By default, this folder is "C:\Program Files\ReliaSoft\Synthesis 9."
** .NET developers – use the SynthesisAPI.dll library
** VB6 / VBA developers – use the SynthesisAPI.tlb library

*The version of the Synthesis Platform that you've installed (32- vs. 64-bit) must match your installed version of Microsoft Office. If they do not match, you may see an [http://www.reliasoft.com/support/rs20024.htm error] related to ActiveX controls.

== API Elements ==

The Synthesis API includes a rich set of programming elements that allow you to work with any of the following components of the Synthesis Platform:

*'''[[Repository Class|Repositories]]''': {{Template:Repository Class.Cmt}}
*'''[[WeibullDataSet Class|Weibull++ Standard Folio]]''': {{Template:WeibullDataSet Class.Cmt}}
*'''[[ALTADataSet Class|ALTA Standard Folio]]''': {{Template:ALTADataSet Class.Cmt}}
*'''[[WAPlots Class|Plots in Weibull++/ALTA]]''': {{Template:WAPlots Class.Cmt}}
*'''[[Resource Classes|Resources]]''': {{Template:Resource Classes.Cmt}}
*'''[[Common Class|Displayed Language]]''': {{Template:Common Class.Cmt}}

A complete list of all the classes and enumerations in the Synthesis API is available [[Full Synthesis API|here]].

== Application Examples ==

'''Excel VBA Samples'''

Use the following links to download macro-enabled Excel files (*.xlsm) that utilize the Synthesis API. Note that to run/view the underlying code, the [http://msdn.microsoft.com/en-us/library/bb608625.aspx Developer tab must be enabled] in Excel so you can enter the Visual Basic for Applications (VBA) environment by choosing '''Developer > View Code'''. Also, you must have [http://office.microsoft.com/en-us/excel-help/enable-or-disable-macros-in-office-documents-HA010031071.aspx macros enabled] to run the example files. If Excel displays a warning regarding macros in these files, select to enable them.
*Use Synthesis analysis engines in Excel
** [http://www.reliasoft.com/synthesis/api/examples/WeibullExample.xlsm Life Data Analysis in Excel (237 KB)] ([[Life Data Analysis in Microsoft Excel - Explanation|Code explanation]])
** [http://www.reliasoft.com/synthesis/api/examples/ALTAExample.xlsm Accelerated Life Testing Analysis (ALTA) in Excel (221 KB)] ([[Accelerated Life Testing Analysis in Microsoft Excel - Explanation|Code explanation]])
* Transfer data from Excel to the Synthesis Reliability Data Warehouse (RDW)
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Standard.xlsm Excel to Standard Repository (2.64 MB)]
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Enterprise.xlsm Excel to Enterprise SQL Repository (2.65 MB)] ''Requires code modification to reference a SQL repository.''
* Use Excel to update Universal Reliability Definitions (URDs) for use in BlockSim, etc.
** [http://www.reliasoft.com/synthesis/api/examples/BlockSimExample.xlsm Update URDs with Excel (108 KB)]

ReliaSoft API Reference

2014-10-15T20:53:39Z

Chris Kahn: /* Application Examples */

{{Template:API|Version 9}}

The Synthesis API can be used to accomplish many of the same tasks as within Synthesis applications, and it also enables seamless integration of the Synthesis Platform with other systems within your organization—all through a programmer's own custom-developed code. This allows you to create customizable and automated solutions to reliability engineering problems by integrating Synthesis functionality into other applications.

This reference describes all of the programming elements in the API. The sample code and documentation have been prepared for the Visual Basic and .NET development environments, and it is assumed that the reader is familiar with them.

== Requirements ==

Before using the Synthesis API, note the following requirements:

*Your code must include a reference to the ReliaSoft Synthesis API Library. The library is located in the folder where ReliaSoft Synthesis is installed. By default, this folder is "C:\Program Files\ReliaSoft\Synthesis 9."
** .NET developers – use the SynthesisAPI.dll library
** VB6 / VBA developers – use the SynthesisAPI.tlb library

*The version of the Synthesis Platform that you've installed (32- vs. 64-bit) must match your installed version of Microsoft Office. If they do not match, you may see an [http://www.reliasoft.com/support/rs20024.htm error] related to ActiveX controls.

== API Elements ==

The Synthesis API includes a rich set of programming elements that allow you to work with any of the following components of the Synthesis Platform:

*'''[[Repository Class|Repositories]]''': {{Template:Repository Class.Cmt}}
*'''[[WeibullDataSet Class|Weibull++ Standard Folio]]''': {{Template:WeibullDataSet Class.Cmt}}
*'''[[ALTADataSet Class|ALTA Standard Folio]]''': {{Template:ALTADataSet Class.Cmt}}
*'''[[WAPlots Class|Plots in Weibull++/ALTA]]''': {{Template:WAPlots Class.Cmt}}
*'''[[Resource Classes|Resources]]''': {{Template:Resource Classes.Cmt}}
*'''[[Common Class|Displayed Language]]''': {{Template:Common Class.Cmt}}

A complete list of all the classes and enumerations in the Synthesis API is available [[Full Synthesis API|here]].

== Application Examples ==

'''Excel VBA Samples'''

Use the following links to download macro-enabled Excel files (*.xlsm) that utilize the Synthesis API. Note that to run/view the underlying code, the [http://msdn.microsoft.com/en-us/library/bb608625.aspx Developer tab must be enabled] in Excel so you can enter the Visual Basic for Applications (VBA) environment by choosing '''Developer > View Code'''. Also, you must have [http://office.microsoft.com/en-us/excel-help/enable-or-disable-macros-in-office-documents-HA010031071.aspx macros enabled] to run the example files. If Excel displays a warning regarding macros in these files, select to enable them.
*Use Synthesis analysis engines in Excel
** [http://www.reliasoft.com/synthesis/api/examples/WeibullExample.xlsm Life Data Analysis in Excel (237KB)] ([[Life Data Analysis in Microsoft Excel - Explanation|Code explanation]])
** [http://www.reliasoft.com/synthesis/api/examples/ALTAExample.xlsm Accelerated Life Testing Analysis (ALTA) in Excel (221 KB)] ([[Accelerated Life Testing Analysis in Microsoft Excel - Explanation|Code explanation]])
* Transfer data from Excel to the Synthesis Reliability Data Warehouse (RDW)
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Standard.xlsm Excel to Standard Repository (2.64MB)]
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Enterprise.xlsm Excel to Enterprise SQL Repository (2.65MB)] ''Requires code modification to reference a SQL repository.''
* Use Excel to update Universal Reliability Definitions (URDs) for use in BlockSim, etc.
** [http://www.reliasoft.com/synthesis/api/examples/BlockSimExample.xlsm Update URDs with Excel (108KB)]

ReliaSoft API Reference

2014-10-15T20:53:25Z

Chris Kahn: /* Application Examples */

{{Template:API|Version 9}}

The Synthesis API can be used to accomplish many of the same tasks as within Synthesis applications, and it also enables seamless integration of the Synthesis Platform with other systems within your organization—all through a programmer's own custom-developed code. This allows you to create customizable and automated solutions to reliability engineering problems by integrating Synthesis functionality into other applications.

This reference describes all of the programming elements in the API. The sample code and documentation have been prepared for the Visual Basic and .NET development environments, and it is assumed that the reader is familiar with them.

== Requirements ==

Before using the Synthesis API, note the following requirements:

*Your code must include a reference to the ReliaSoft Synthesis API Library. The library is located in the folder where ReliaSoft Synthesis is installed. By default, this folder is "C:\Program Files\ReliaSoft\Synthesis 9."
** .NET developers – use the SynthesisAPI.dll library
** VB6 / VBA developers – use the SynthesisAPI.tlb library

*The version of the Synthesis Platform that you've installed (32- vs. 64-bit) must match your installed version of Microsoft Office. If they do not match, you may see an [http://www.reliasoft.com/support/rs20024.htm error] related to ActiveX controls.

== API Elements ==

The Synthesis API includes a rich set of programming elements that allow you to work with any of the following components of the Synthesis Platform:

*'''[[Repository Class|Repositories]]''': {{Template:Repository Class.Cmt}}
*'''[[WeibullDataSet Class|Weibull++ Standard Folio]]''': {{Template:WeibullDataSet Class.Cmt}}
*'''[[ALTADataSet Class|ALTA Standard Folio]]''': {{Template:ALTADataSet Class.Cmt}}
*'''[[WAPlots Class|Plots in Weibull++/ALTA]]''': {{Template:WAPlots Class.Cmt}}
*'''[[Resource Classes|Resources]]''': {{Template:Resource Classes.Cmt}}
*'''[[Common Class|Displayed Language]]''': {{Template:Common Class.Cmt}}

A complete list of all the classes and enumerations in the Synthesis API is available [[Full Synthesis API|here]].

== Application Examples ==

'''Excel VBA Samples'''

Use the following links to download macro-enabled Excel files (*.xlsm) that utilize the Synthesis API. Note that to run/view the underlying code, the [http://msdn.microsoft.com/en-us/library/bb608625.aspx Developer tab must be enabled] in Excel so you can enter the Visual Basic for Applications (VBA) environment by choosing '''Developer > View Code'''. Also, you must have [http://office.microsoft.com/en-us/excel-help/enable-or-disable-macros-in-office-documents-HA010031071.aspx macros enabled] to run the example files. If Excel displays a warning regarding macros in these files, select to enable them.
*Use Synthesis analysis engines in Excel
** [http://www.reliasoft.com/synthesis/api/examples/WeibullExample.xlsm Life Data Analysis in Excel (237KB)] ([[Life Data Analysis in Microsoft Excel - Explanation|Code explanation]])
** [http://www.reliasoft.com/synthesis/api/examples/ALTAExample.xlsm Accelerated Life Testing Analysis (ALTA) in Excel (221 KB)] ([[Accelerated Life Testing Analysis in Microsoft Excel - Explanation|Code explanation]])
* Transfer data from Excel to the Synthesis Reliability Data Warehouse (RDW)
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Standard.xlsm Excel to Standard Repository (2.64MB)]
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Enterprise.xlsm Excel to Enterprise SQL Repository (2.65MB)] ''Requires code modification to reference a SQL repository.''
* Use Excel to update Universal Reliability Definitions (URDs) for use in BlockSim, etc.
** [http://www.reliasoft.com/synthesis/api/examples/BlockSimExample.xlsm Update URDs in Excel (108KB)]

ReliaSoft API Reference

2014-10-15T20:53:09Z

Chris Kahn: /* Application Examples */

{{Template:API|Version 9}}

The Synthesis API can be used to accomplish many of the same tasks as within Synthesis applications, and it also enables seamless integration of the Synthesis Platform with other systems within your organization—all through a programmer's own custom-developed code. This allows you to create customizable and automated solutions to reliability engineering problems by integrating Synthesis functionality into other applications.

This reference describes all of the programming elements in the API. The sample code and documentation have been prepared for the Visual Basic and .NET development environments, and it is assumed that the reader is familiar with them.

== Requirements ==

Before using the Synthesis API, note the following requirements:

*Your code must include a reference to the ReliaSoft Synthesis API Library. The library is located in the folder where ReliaSoft Synthesis is installed. By default, this folder is "C:\Program Files\ReliaSoft\Synthesis 9."
** .NET developers – use the SynthesisAPI.dll library
** VB6 / VBA developers – use the SynthesisAPI.tlb library

*The version of the Synthesis Platform that you've installed (32- vs. 64-bit) must match your installed version of Microsoft Office. If they do not match, you may see an [http://www.reliasoft.com/support/rs20024.htm error] related to ActiveX controls.

== API Elements ==

The Synthesis API includes a rich set of programming elements that allow you to work with any of the following components of the Synthesis Platform:

*'''[[Repository Class|Repositories]]''': {{Template:Repository Class.Cmt}}
*'''[[WeibullDataSet Class|Weibull++ Standard Folio]]''': {{Template:WeibullDataSet Class.Cmt}}
*'''[[ALTADataSet Class|ALTA Standard Folio]]''': {{Template:ALTADataSet Class.Cmt}}
*'''[[WAPlots Class|Plots in Weibull++/ALTA]]''': {{Template:WAPlots Class.Cmt}}
*'''[[Resource Classes|Resources]]''': {{Template:Resource Classes.Cmt}}
*'''[[Common Class|Displayed Language]]''': {{Template:Common Class.Cmt}}

A complete list of all the classes and enumerations in the Synthesis API is available [[Full Synthesis API|here]].

== Application Examples ==

'''Excel VBA Samples'''

Use the following links to download macro-enabled Excel files (*.xlsm) that utilize the Synthesis API. Note that to run/view the underlying code, the [http://msdn.microsoft.com/en-us/library/bb608625.aspx Developer tab must be enabled] in Excel so you can enter the Visual Basic for Applications (VBA) environment by choosing '''Developer > View Code'''. Also, you must have [http://office.microsoft.com/en-us/excel-help/enable-or-disable-macros-in-office-documents-HA010031071.aspx macros enabled] to run the example files. If Excel displays a warning regarding macros in these files, select to enable them.
*Use Synthesis analysis engines in Excel
** [http://www.reliasoft.com/synthesis/api/examples/WeibullExample.xlsm Life Data Analysis in Excel (237KB)] ([[Life Data Analysis in Microsoft Excel - Explanation|Code explanation]])
** [http://www.reliasoft.com/synthesis/api/examples/ALTAExample.xlsm Accelerated Life Testing Analysis (ALTA) in Excel (221 KB)] ([[Accelerated Life Testing Analysis in Microsoft Excel - Explanation|Code explanation]])
* Transfer data from Excel to the Synthesis Reliability Data Warehouse (RDW)
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Standard.xlsm Excel to Standard Repository (2.64MB)]
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Enterprise.xlsm Excel to Enterprise SQL Repository (2.65MB)] ''Requires code modification to reference a SQL repository.''
* Use Excel to update Universal Reliability Definitions (URDs) for use in BlockSim, etc.
** [http://www.reliasoft.com/synthesis/api/examples/BlockSimExample.xlsm Update URDs in Excel(108KB)]

ReliaSoft API Reference

2014-10-15T20:50:34Z

Chris Kahn: /* Application Examples */

{{Template:API|Version 9}}

The Synthesis API can be used to accomplish many of the same tasks as within Synthesis applications, and it also enables seamless integration of the Synthesis Platform with other systems within your organization—all through a programmer's own custom-developed code. This allows you to create customizable and automated solutions to reliability engineering problems by integrating Synthesis functionality into other applications.

This reference describes all of the programming elements in the API. The sample code and documentation have been prepared for the Visual Basic and .NET development environments, and it is assumed that the reader is familiar with them.

== Requirements ==

Before using the Synthesis API, note the following requirements:

*Your code must include a reference to the ReliaSoft Synthesis API Library. The library is located in the folder where ReliaSoft Synthesis is installed. By default, this folder is "C:\Program Files\ReliaSoft\Synthesis 9."
** .NET developers – use the SynthesisAPI.dll library
** VB6 / VBA developers – use the SynthesisAPI.tlb library

*The version of the Synthesis Platform that you've installed (32- vs. 64-bit) must match your installed version of Microsoft Office. If they do not match, you may see an [http://www.reliasoft.com/support/rs20024.htm error] related to ActiveX controls.

== API Elements ==

The Synthesis API includes a rich set of programming elements that allow you to work with any of the following components of the Synthesis Platform:

*'''[[Repository Class|Repositories]]''': {{Template:Repository Class.Cmt}}
*'''[[WeibullDataSet Class|Weibull++ Standard Folio]]''': {{Template:WeibullDataSet Class.Cmt}}
*'''[[ALTADataSet Class|ALTA Standard Folio]]''': {{Template:ALTADataSet Class.Cmt}}
*'''[[WAPlots Class|Plots in Weibull++/ALTA]]''': {{Template:WAPlots Class.Cmt}}
*'''[[Resource Classes|Resources]]''': {{Template:Resource Classes.Cmt}}
*'''[[Common Class|Displayed Language]]''': {{Template:Common Class.Cmt}}

A complete list of all the classes and enumerations in the Synthesis API is available [[Full Synthesis API|here]].

== Application Examples ==

'''Excel VBA Samples'''

Use the following links to download macro-enabled Excel files (*.xlsm) that utilize the Synthesis API. Note that to run/view the underlying code, the [http://msdn.microsoft.com/en-us/library/bb608625.aspx Developer tab must be enabled] in Excel so you can enter the Visual Basic for Applications (VBA) environment by choosing '''Developer > View Code'''. Also, you must have [http://office.microsoft.com/en-us/excel-help/enable-or-disable-macros-in-office-documents-HA010031071.aspx macros enabled] to run the example files. If Excel displays a warning regarding macros in these files, select to enable them.
*Use Synthesis analysis engines in Excel
** [http://www.reliasoft.com/synthesis/api/examples/WeibullExample.xlsm Life Data Analysis in Excel (237KB)] ([[Life Data Analysis in Microsoft Excel - Explanation|Code explanation]])
** [http://www.reliasoft.com/synthesis/api/examples/ALTAExample.xlsm Accelerated Life Testing Analysis (ALTA) in Excel (221 KB)] ([[Accelerated Life Testing Analysis in Microsoft Excel - Explanation|Code explanation]])
* Transfer data from Excel to the Synthesis Reliability Data Warehouse (RDW)
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Standard.xlsm Excel to Standard Repository (2.64MB)]
** [http://www.reliasoft.com/synthesis/api/examples/RDW_Example_Enterprise.xlsm Excel to Enterprise SQL Repository (2.65MB)] ''Requires code modification to reference a SQL repository.''
* Use Excel to update Universal Reliability Definitions (URDs) for use in BlockSim, etc.
** [http://www.reliasoft.com/synthesis/api/examples/BlockSimExample.xlsm URD Update Tool (108KB)]

ModelTypeEnum Enumeration

2014-06-25T20:13:08Z

Chris Kahn:

{{Template:APIClass|cModel_Class|cModel}}
Specifies the type (e.g., 2-parameter Weibull) for a [[cModel Class|cModel]] object.

Note that only some types can be created using API calls. See [[CModel Constructors|cModel Constructors]]. Other types must be created within a Synthesis desktop application.

== Members ==
'''Weibull++'''

''Models of these types can be created using API calls''
* Weibull1
* Weibull2
* Weibull3
* MixedWeibull2
* MixedWeibull3
* MixedWeibull4
* Exponential1
* Exponential2
* Normal
* Lognormal
* GenGamma
* Gamma
* Logistic
* LogLogistic
* Gumbel

''These models cannot be created using API calls''
* WeibullBayesian_NormalPrior
* WeibullBayesian_LognormalPrior
* WeibullBayesian_ExponentialPrior
* WeibullBayesian_UniformPrior
* WeibullCFM
* NormalCFM
* LognormalCFM
* ExponentialCFM
* GenGammaCFM
* GammaCFM
* LogisticCFM
* LogLogisticCFM
* GumbelCFM

'''ALTA'''

''These models cannot be created using API calls''
* ArrheniusWeibull
* ArrheniusLognormal
* ArrheniusExponential
* EyringWeibull
* EyringLognormal
* EyringExponential
* IPLWeibull
* IPLLognormal
* IPLExponential
* THWeibull
* THLognormal
* THExponential
* TNTWeibull
* TNTLognormal
* TNTExponential
* GeneralizedEyringWeibull
* GeneralizedEyringLognormal
* GeneralizedEyringExponential
* ProportionalHazardsWeibull
* ProportionalHazardsExponential
* GeneralLogLinearWeibull
* GeneralLogLinearLognormal
* GeneralLogLinearExponential
* CumulativeDamageWeibull
* CumulativeDamageLognormal
* CumulativeDamageExponential

'''BlockSim'''

''These models can be created using API calls''
* FixedUnreliability
* FixedDuration
* FixedCost

''This model cannot be created using API calls''
* DiagramAnalysis

ModelTypeEnum Enumeration

2014-06-25T18:46:50Z

Chris Kahn:

ModelTypeEnum Enumeration

2014-06-25T18:46:04Z

Chris Kahn:

{{Template:APIClass|cModel_Class|cModel}}
Specifies the type (e.g., 2-parameter Weibull) for a [[cModel Class|cModel]] object.

Note that only some types can be created using API calls. See [[CModel Constructors|cModel Constructors]]. Other types must be created within the user interface of a Synthesis application.

== Members ==
'''Weibull++'''

''Models of these types can be created using API calls''
* Weibull1
* Weibull2
* Weibull3
* MixedWeibull2
* MixedWeibull3
* MixedWeibull4
* Exponential1
* Exponential2
* Normal
* Lognormal
* GenGamma
* Gamma
* Logistic
* LogLogistic
* Gumbel

''These models cannot be created via API calls''
* WeibullBayesian_NormalPrior
* WeibullBayesian_LognormalPrior
* WeibullBayesian_ExponentialPrior
* WeibullBayesian_UniformPrior
* WeibullCFM
* NormalCFM
* LognormalCFM
* ExponentialCFM
* GenGammaCFM
* GammaCFM
* LogisticCFM
* LogLogisticCFM
* GumbelCFM

'''ALTA'''

''These models cannot be created using API calls''
* ArrheniusWeibull
* ArrheniusLognormal
* ArrheniusExponential
* EyringWeibull
* EyringLognormal
* EyringExponential
* IPLWeibull
* IPLLognormal
* IPLExponential
* THWeibull
* THLognormal
* THExponential
* TNTWeibull
* TNTLognormal
* TNTExponential
* GeneralizedEyringWeibull
* GeneralizedEyringLognormal
* GeneralizedEyringExponential
* ProportionalHazardsWeibull
* ProportionalHazardsExponential
* GeneralLogLinearWeibull
* GeneralLogLinearLognormal
* GeneralLogLinearExponential
* CumulativeDamageWeibull
* CumulativeDamageLognormal
* CumulativeDamageExponential

'''BlockSim'''

''These models can be created using API calls''
* FixedUnreliability
* FixedDuration
* FixedCost
* DiagramAnalysis

ModelTypeEnum Enumeration

2014-06-25T18:41:11Z

Chris Kahn:

{{Template:APIClass|cModel_Class|cModel}}
Specifies the type (e.g., 2-parameter Weibull) for a [[cModel Class|cModel]] object.

Note that only the types marked with an asterisk (*) can be created using API calls. See [[CModel Constructors|cModel Constructors]]. Other types must be created within the user interface of a Synthesis application.

== Members ==
'''Weibull++'''
* Weibull1*
* Weibull2*
* Weibull3*
* MixedWeibull2*
* MixedWeibull3*
* MixedWeibull4*
* Exponential1*
* Exponential2*
* Normal*
* Lognormal*
* GenGamma*
* Gamma*
* Logistic*
* LogLogistic*
* Gumbel*
<div style="color: #909090">
* WeibullBayesian_NormalPrior
* WeibullBayesian_LognormalPrior
* WeibullBayesian_ExponentialPrior
* WeibullBayesian_UniformPrior
* WeibullCFM
* NormalCFM
* LognormalCFM
* ExponentialCFM
* GenGammaCFM
* GammaCFM
* LogisticCFM
* LogLogisticCFM
* GumbelCFM
</div>
'''ALTA'''
<div style="color: #909090">
* ArrheniusWeibull
* ArrheniusLognormal
* ArrheniusExponential
* EyringWeibull
* EyringLognormal
* EyringExponential
* IPLWeibull
* IPLLognormal
* IPLExponential
* THWeibull
* THLognormal
* THExponential
* TNTWeibull
* TNTLognormal
* TNTExponential
* GeneralizedEyringWeibull
* GeneralizedEyringLognormal
* GeneralizedEyringExponential
* ProportionalHazardsWeibull
* ProportionalHazardsExponential
* GeneralLogLinearWeibull
* GeneralLogLinearLognormal
* GeneralLogLinearExponential
* CumulativeDamageWeibull
* CumulativeDamageLognormal
* CumulativeDamageExponential
</div>
'''BlockSim'''
* FixedUnreliability*
* FixedDuration*
* FixedCost*
* DiagramAnalysis*

*Only models of these types can be created using API calls.

CModel Constructors

2014-06-25T18:40:07Z

Chris Kahn:

{{Template:APIClass|cModel_Class|cModel}}{{DISPLAYTITLE:cModel Constructors}}
Constructors for the [[cModel_Class|cModel]] class.

== Syntax ==
*cModel() {{APIComment|{{Template:cModel_Constructors1.Cmt}}}}
*cModel( ModelType{{APIPrefix|As ModelTypeEnum}}, ModelCategory {{APIPrefix|As ModelCategoryEnum}}, ModelName {{APIPrefix|As String}},{{APIPrefix|ParamArray}} ModelParams(){{APIPrefix|As Double}}) {{APIComment|{{Template:cModel_Constructors2.Cmt}}}}

Parameters
:''ModelType'': The type of model (e.g., 2-parameter Weibull), specified with a ModelTypeEnum enumeration value. Note that some models cannot be created through the API (i.e., some can be created only within the user interface of a Synthesis application). See [[ModelTypeEnum Enumeration|ModelTypeEnum]].
:''ModelCategory'': The model category (e.g., reliability model), specified with a [[ModelCategoryEnum Enumeration|ModelCategoryEnum]] value.
:''ModelName'': The model name.
:''ModelParams()'': An array of parameter values. 

== Usage Example ==
{{APIComment|'Declare the cModel class using a pre-defined parameter list.}}
Dim newParams(1) As Double
newParams(0) = 1
newParams(1) = 100
Dim newModel As New cModel(ModelTypeEnum.Weibull2,
ModelCategoryEnum.Reliability, "NewModel1", newParams)

{{APIComment|'Alternatively, declare the cModel class using an in-line parameter list.}}
Dim newModel As New cModel(ModelTypeEnum.Weibull2,
ModelCategoryEnum.Reliability, "NewModel1", 1, 100)

ModelTypeEnum Enumeration

2014-06-25T18:39:08Z

Chris Kahn: /* Members */

ModelTypeEnum Enumeration

2014-06-25T18:32:01Z

Chris Kahn: /* Members */

{{Template:APIClass|cModel_Class|cModel}}
Specifies the type (e.g., 2-parameter Weibull) for a [[cModel Class|cModel]] object.

Note that only the types marked with an asterisk (*) can be created using API calls. See [[CModel Constructors|cModel Constructors]]. Other types must be created within the user interface of a Synthesis application.

== Members ==
'''Weibull++'''
* Weibull1*
* Weibull2*
* Weibull3*
* MixedWeibull2*
* MixedWeibull3*
* MixedWeibull4*
* Exponential1*
* Exponential2*
* Normal*
* Lognormal*
* GenGamma*
* Gamma*
* Logistic*
* LogLogistic*
* Gumbel*
* WeibullBayesian_NormalPrior
* WeibullBayesian_LognormalPrior
* WeibullBayesian_ExponentialPrior
* WeibullBayesian_UniformPrior
* WeibullCFM
* NormalCFM
* LognormalCFM
* ExponentialCFM
* GenGammaCFM
* GammaCFM
* LogisticCFM
* LogLogisticCFM
* GumbelCFM

'''ALTA'''
* ArrheniusWeibull
* ArrheniusLognormal
* ArrheniusExponential
* EyringWeibull
* EyringLognormal
* EyringExponential
* IPLWeibull
* IPLLognormal
* IPLExponential
* THWeibull
* THLognormal
* THExponential
* TNTWeibull
* TNTLognormal
* TNTExponential
* GeneralizedEyringWeibull
* GeneralizedEyringLognormal
* GeneralizedEyringExponential
* ProportionalHazardsWeibull
* ProportionalHazardsExponential
* GeneralLogLinearWeibull
* GeneralLogLinearLognormal
* GeneralLogLinearExponential
* CumulativeDamageWeibull
* CumulativeDamageLognormal
* CumulativeDamageExponential

'''BlockSim'''
* FixedUnreliability*
* FixedDuration*
* FixedCost*
* DiagramAnalysis*

*Only these model types can be created using API calls.

Hypothesis Tests

2014-06-12T17:51:35Z

Chris Kahn: /* Common Beta Hypothesis Example */

{{Template:RGA_BOOK_SUB|Appendix B|Hypothesis Tests}}
==Common Beta Hypothesis Test==
The common beta hypothesis (CBH) test is applicable to the following data types: multiple systems-concurrent operating times, repairable and fleet. As shown by Crow [[RGA_References|[17]]], suppose that <math>K\,\!</math> number of systems are under test. Each system has an intensity function given by:

:<math>{{u}_{q}}(t)={{\lambda }_{q}}{{\beta }_{q}}{{t}^{{{\beta }_{q}}-1}}\,\!</math>

where <math>q=1,\ldots ,K\,\!</math>. You can compare the intensity functions of each of the systems by comparing the <math>{{\beta }_{q}}\,\!</math> of each system. When conducting an analysis of data consisting of multiple systems, you expect that each of the systems performed in a similar manner. In particular, you would expect the interarrival rate of the failures across the systems to be fairly consistent. Therefore, the CBH test evaluates the hypothesis, <math>{{H}_{o}}\,\!</math>, such that <math>{{\beta }_{1}}={{\beta }_{2}}=\ldots ={{\beta }_{K}}\,\!</math>. Let <math>{{\tilde{\beta }}_{q}}\,\!</math> denote the conditional maximum likelihood estimate of <math>{{\beta }_{q}}\,\!</math>, which is given by:

:<math>{{\tilde{\beta }}_{q}}=\frac{\underset{q=1}{\overset{K}{\mathop{\sum }}}\,{{M}_{q}}}{\underset{q=1}{\overset{K}{\mathop{\sum }}}\,\underset{i=1}{\overset{{{M}_{q}}}{\mathop{\sum }}}\,\ln \left( \tfrac{{{T}_{q}}}{{{X}_{iq}}} \right)}\,\!</math>

where:

*<math>K=1.\,\!</math>
*<math>{{M}_{q}}={{N}_{q}}\,\!</math> if data on the <math>{{q}^{th}}\,\!</math> system is time terminated or <math>{{M}_{q}}=({{N}_{q}}-1)\,\!</math> if data on the <math>{{q}^{th}}\,\!</math> system is failure terminated ( <math>{{N}_{q}}\,\!</math> is the number of failures on the <math>{{q}^{th}}\,\!</math> system).
*<math>{{X}_{iq}}\,\!</math> is the <math>{{i}^{th}}\,\!</math> time-to-failure on the <math>{{q}^{th}}\,\!</math> system.

Then for each system, assume that:

:<math>\chi _{q}^{2}=\frac{2{{M}_{q}}{{\beta }_{q}}}{{{{\tilde{\beta }}}_{q}}}\,\!</math>

are conditionally distributed as independent chi-squared random variables with <math>2{{M}_{q}}\,\!</math> degrees of freedom. When <math>K=2\,\!</math>, you can test the null hypothesis, <math>{{H}_{o}}\,\!</math>, using the following statistic:

:<math>F=\frac{\tfrac{\chi _{1}^{2}}{2{{M}_{1}}}}{\tfrac{\chi _{2}^{2}}{2{{M}_{2}}}}\,\!</math>

If <math>{{H}_{o}}\,\!</math> is true, then <math>F\,\!</math> equals <math>\tfrac{{{{\tilde{\beta }}}_{2}}}{{{{\tilde{\beta }}}_{1}}}\,\!</math> and conditionally has an F-distribution with <math>(2{{M}_{1}},2{{M}_{2}})\,\!</math> degrees of freedom. The critical value, <math>F\,\!</math>, can then be determined by referring to the chi-squared tables. Now, if <math>K\ge 2\,\!</math>, then the likelihood ratio procedure can be used to test the hypothesis <math>{{\beta }_{1}}={{\beta }_{2}}=\ldots ={{\beta }_{K}}\,\!</math>, as discussed in Crow [[RGA_References|[17]]]. Consider the following statistic:

:<math>L=\underset{q=1}{\overset{K}{\mathop \sum }}\,{{M}_{q}}\ln ({{\tilde{\beta }}_{q}})-M\ln ({{\beta }^{*}})\,\!</math>

where:

*<math>M=\underset{q=1}{\overset{K}{\mathop{\sum }}}\,{{M}_{q}}\,\!</math>
*<math>{{\beta }^{*}}=\tfrac{M}{\underset{q=1}{\overset{K}{\mathop{\sum }}}\,\tfrac{{{M}_{q}}}{{{{\tilde{\beta }}}_{q}}}}\,\!</math>

Also, let:

:<math>a=1+\frac{1}{6(K-1)}\left[ \underset{q=1}{\overset{K}{\mathop \sum }}\,\frac{1}{{{M}_{q}}}-\frac{1}{M} \right]\,\!</math>

Calculate the statistic <math>D\,\!</math>, such that:

:<math>D=\frac{2L}{a}\,\!</math>

The statistic <math>D\,\!</math> is approximately distributed as a chi-squared random variable with <math>(K-1)\,\!</math> degrees of freedom. Then after calculating <math>D\,\!</math>, refer to the chi-squared tables with <math>(K-1)\,\!</math> degrees of freedom to determine the critical points. <math>{{H}_{o}}\,\!</math> is true if the statistic <math>D\,\!</math> falls between the critical points.

===Common Beta Hypothesis Example===

Consider the data in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Repairable System Data'''
|-
| ||System 1||System 2||System 3
|-
|Start||0||0||0
|-
|End||2000||2000||2000
|-
|Failures||1.2||1.4||0.3
|-
| ||55.6 ||35 ||32.6
|-
| ||72.7||46.8||33.4
|-
| ||111.9||65.9||241.7
|-
| ||121.9||181.1||396.2
|-
| ||303.6||712.6||444.4
|-
| ||326.9||1005.7||480.8
|-
| ||1568.4||1029.9||588.9
|-
| ||1913.5||1675.7||1043.9
|-
| || ||1787.5||1136.1
|-
| || ||1867||1288.1
|-
| || || ||1408.1
|-
| || || ||1439.4
|-
| || || ||1604.8
|}

Given that the intensity function for the <math>{{q}^{th}}\,\!</math> system is <math>{{u}_{q}}(t)={{\lambda }_{q}}{{\beta }_{q}}{{t}^{{{\beta }_{q}}-1}}\,\!</math>, test the hypothesis that <math>{{\beta }_{1}}={{\beta }_{2}}\,\!</math> while assuming a significance level equal to 0.05. Calculate the maximum likelihood estimates of <math>{{\tilde{\beta }}_{1}}\,\!</math> and <math>{{\tilde{\beta }}_{2}}\,\!</math>. Therefore:

:<math>\begin{align}
& {{{\tilde{\beta }}}_{1}}= & 0.3753 \\
& {{{\tilde{\beta }}}_{2}}= & 0.4657
\end{align}\,\!</math>

Then <math>\tfrac{{{{\tilde{\beta }}}_{2}}}{{{{\tilde{\beta }}}_{1}}}=1.2408\,\!</math>. Calculate the statistic <math>F\,\!</math> with a significance level of 0.05.

:<math>\begin{align}
F=2.0980
\end{align}\,\!</math>

Since <math>1.2408<2.0980\,\!</math> we fail to reject the null hypothesis that <math>{{\beta }_{1}}={{\beta }_{2}}\,\!</math> at the 5% significance level.

Now suppose that we test the hypothesis that <math>{{\beta }_{1}}={{\beta }_{2}}={{\beta }_{3}}\,\!</math>. Calculate the statistic <math>D\,\!</math>.

:<math>\begin{align}
D=0.5260
\end{align}\,\!</math>

Using the chi-square tables with <math>K-1=2\,\!</math> degrees of freedom, the critical values at the 2.5 and 97.5 percentiles are 0.1026 and 5.9915, respectively. Since <math>0.1026<D<5.9915\,\!</math>, we fail to reject the null hypothesis that <math>{{\beta }_{1}}={{\beta }_{2}}={{\beta }_{3}}\,\!</math> at the 5% significance level.

==Laplace Trend Test==
The Laplace trend test evaluates the hypothesis that a trend does not exist within the data. The Laplace trend test is applicable to the following data types: multiple systems-concurrent operating times, repairable and fleet. The Laplace trend test can determine whether the system is deteriorating, improving, or if there is no trend at all. Calculate the test statistic, <math>U\,\!</math>, using the following equation:

:<math>U=\frac{\tfrac{\underset{i=1}{\overset{N}{\mathop{\sum }}}\,{{X}_{i}}}{N}-\tfrac{T}{2}}{T\sqrt{\tfrac{1}{12N}}}\,\!</math>

where:

*<math>T\,\!</math> = total operating time (termination time)
*<math>{{X}_{i}}\,\!</math> = age of the system at the <math>{{i}^{th}}\,\!</math> successive failure
*<math>N\,\!</math> = total number of failures

The test statistic <math>U\,\!</math> is approximately a standard normal random variable. The critical value is read from the standard normal tables with a given significance level, <math>\alpha \,\!</math>.

===Laplace Trend Test Example===

Consider once again the data given in the table above. Check for a trend within System 1 assuming a significance level of 0.10. Calculate the test statistic <math>U\,\!</math> for System 1.

:<math>\begin{align}
U=-2.6121
\end{align}\,\!</math>

From the standard normal tables with a significance level of 0.10, the critical value is equal to 1.645. If <math>-1.645<U<1.645\,\!</math> then we would fail to reject the hypothesis of no trend. However, since <math>U<-1.645\,\!</math> then an improving trend exists within System 1. If <math>U>1.645\,\!</math> then a deteriorating trend would exist.

Failure Discounting Example

2014-06-12T17:50:51Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the article [[Failure Discounting]]''.
</noinclude>

Assume that during the 22 launches given in the first table below, the first failure was caused by Mode 1, the second and fourth failures were caused by Mode 2, the third and fifth failures were caused by Mode 3, the sixth failure was caused by Mode 4 and the seventh failure was caused by Mode 5.

#Find the standard Gompertz reliability growth curve using the results of the first 15 launches.
#Find the predicted reliability after launch 22.
#Calculate the reliability after launch 22 based on the full data set from the second table, and compare it with the estimate obtained for question 2.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="10" style="text-align:center"|'''Launch Sequence with Failure Modes and Failure Values'''
|-
!Launch Number
!Result/Mode
!Failure 1
!Failure 2
!Failure 3
!Failure 4
!Failure 5
!Failure 6
!Failure 7
!Sum of Failures
|-
|1|| F1|| 1.000|| || || || || || || 1.000
|-
|2|| F2|| 1.000|| 1.000 || || || || || || 2.000
|-
|3|| F3|| 0.900|| 1.000|| 1.000|| || || || || 2.900
|-
|4|| S|| 0.684|| 0.900|| 1.000|| || || || || 2.584
|-
|5|| F2|| 0.536|| 1.000|| 0.900|| 1.000|| || || || 3.436
|-
|6|| F3|| 0.438|| 1.000|| 1.000|| 1.000|| 1.000|| || || 4.438
|-
|7|| S|| 0.369|| 0.900|| 1.000|| 0.900|| 1.000|| || || 4.169
|-
|8|| S|| 0.319|| 0.684|| 0.900|| 0.684|| 0.900|| || || 3.486
|-
|9|| S|| 0.280|| 0.536|| 0.684|| 0.536|| 0.684|| || || 2.720
|-
|10|| S|| 0.250|| 0.438|| 0.536|| 0.438|| 0.536|| || || 2.197
|-
|11|| S|| 0.226|| 0.369|| 0.438|| 0.369|| 0.438|| || || 1.839
|-
|12|| S|| 0.206|| 0.319|| 0.369|| 0.319|| 0.369|| || || 1.581
|-
|13|| S|| 0.189|| 0.280|| 0.319|| 0.280|| 0.319|| || || 1.387
|-
|14|| S|| 0.175|| 0.250|| 0.280|| 0.250|| 0.280|| || || 1.235
|-
|15|| S|| 0.162|| 0.226|| 0.250|| 0.226|| 0.250|| || || 1.114
|-
|16|| S|| 0.152|| 0.206|| 0.226|| 0.206|| 0.226|| || || 1.014
|-
|17|| F4|| 0.142|| 0.189|| 0.206|| 0.189|| 0.206|| 1.000|| || 1.931
|-
|18|| S|| 0.134|| 0.175|| 0.189|| 0.175|| 0.189|| 1.000|| || 1.861
|-
|19|| F5|| 0.127|| 0.162|| 0.175|| 0.162|| 0.175|| 0.900|| 1.000|| 2.701
|-
|20|| S|| 0.120|| 0.152|| 0.162|| 0.152|| 0.162|| 0.684|| 1.000|| 2.432
|-
|21|| S|| 0.114|| 0.142|| 0.152|| 0.142|| 0.152|| 0.536|| 0.900|| 2.138
|-
|22|| S|| 0.109|| 0.134|| 0.142|| 0.134|| 0.142|| 0.438|| 0.684|| 1.783
|}

 

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Comparison of the Predicted Reliability with the Actual Data'''
|-
!Launch Number
!Calculated Reliability (%)
!ln(R)
!Gompertz Reliability (%)
|-
|1|| 0.000|| ||
|-
|2|| 0.000|| ||
|-
|3|| 3.333|| 1.204||
|-
|4|| 35.406|| 3.567|| 16.426
|-
|5|| 31.283|| 3.443|| 26.691
|-
|6|| 26.039|| 3.260|| 37.858
|-
|7|| 40.442|| 3.670|| 48.691
|-
|8|| 56.422|| 4.033|| 58.363
|-
|9|| 69.783|| 4.245|| 66.496
|-
| || || <math>{{S}_{1}}\,\!</math> = 22.218 ||
|-
|10|| 78.029 ||4.357 ||73.044
|-
|11|| 83.281 ||4.422 ||78.155
|-
|12|| 86.824 ||4.464 ||82.055
|-
|13|| 89.331|| 4.492|| 84.983
|-
|14|| 91.175|| 4.513|| 87.155
|-
|15|| 92.573|| 4.528|| 88.754
|-
| || || <math>{{S}_{2}}\,\!</math> = 26.776||
|-
|16|| 93.660|| 4.540|| 89.923
|-
|17|| 88.639|| 4.484|| 90.774
|-
|18|| 89.661|| 4.496 ||91.392
|-
|19|| 85.787|| 4.452|| 91.839
|-
|20|| 87.841|| 4.476 ||92.163
|-
|21|| 89.820|| 4.498|| 92.396
|-
| || || <math>{{S}_{3}}\,\!</math> = 26.946||
|-
|22|| 91.896 4.521 92.565|| ||
|}

'''Solution'''
<ol>
<li>In the table above, the failures are represented by columns "Failure 1", "Failure 2", etc. The "Result/Mode" column shows whether each launch is a failure (indicated by the failure modes F1, F2, etc.) or a success (S). The values of failure are based on <math>CL=0.90\,\!</math> and are calculated from:

:<math>f=1-{{(1-CL)}^{\tfrac{1}{{{S}_{n}}}}}\,\!</math>

These values are summed and the reliability is calculated from:

:<math>R=\left[ 1-\left( \frac{\mathop{}_{i=1}^{N}{{f}_{i}}}{n} \right) \right]\cdot 100\text{ }%\,\!</math>

where <math>N\,\!</math> is the number of failures and <math>n\,\!</math> is the number of events, tests, runs or launches.

*Failure 1 is Mode 1; it occurs at launch 1 and it does not recur throughout the process. So at launch 3, <math>{{S}_{n}}=1\,\!</math>, and so on.

*Failure 2 is Mode 2; it occurs at launch 2 and it recurs at launch 5. Therefore, <math>{{S}_{n}}=1\,\!</math> at launch 4 and at launch 7, and so on.

*Failure 3 is Mode 3; it occurs at launch 3 and it recurs at launch 6. Therefore, <math>{{S}_{n}}=1\,\!</math> at launch 5 and at launch 8, and so on.

*Failure 6 is Mode 4; it occurs at launch 17 and it does not recur throughout the process. So at launch 19, <math>{{S}_{n}}=1\,\!</math>, and so on.

*Failure 7 is Mode 5; it occurs at launch 19 and it does not recur throughout the process. So at launch 21, <math>{{S}_{n}}=1\,\!</math>, and so on.

For launch 3 and failure 1, <math>{{S}_{n}}=1\,\!</math>.

:<math>\begin{align}
{{f}_{1/3}}=1-{{(1-0.90)}^{1/1}}=0.900
\end{align}\,\!</math>

For launch 4 and failure 1, <math>{{S}_{n}}=2\,\!</math>.

:<math>\begin{align}
{{f}_{1/4}}=1-{{(1-0.90)}^{1/2}}=0.684
\end{align}\,\!</math>

And so on.

Calculate the initial values of the Gompertz parameters using the second table above. Based on the equations from the [[Gompertz Models]] chapter, the initial values are:

:<math>\begin{align}
c &= \left ( \frac{S_{3}-S_{2}}{S_{2}-S_{1}} \right )^\frac{1}{n\cdot I} \\
&= \left [ \frac{26.946-26.776}{26.776-22.218} \right ]^\frac{1}{6} \\
&= 0.578 \\
\end{align}\,\!</math>

:<math>\begin{align}
a &= e^\left [\frac{1}{n}\left (S_{1} + \frac {S_{2}-S_{1}}{1-e^{n\cdot I}} \right )\right ] \\
&= e^\left [\frac{1}{6}\left (22.218 + \frac{26.776 - 22.218}{1-0.578^{6}}\right ) \right ] \\
&= 89.31% \\
\end{align}\,\!</math>

:<math>\begin{align}
b &= e^\left [\frac{(S_{2}-S_{1})(c-1)}{(1-c^{n})^{2}} \right ] \\
&= e^\left [\frac{(26.776-22.218)(0.578-1)}{(1-0.578^{6})^{2}} \right ] \\
&= 0.127 \\
\end{align}\,\!</math>

Now, since the initial values have been determined, the Gauss-Newton method can be used. Substituting <math>{{Y}_{i}}={{R}_{i}},\,\!</math> <math>g_{1}^{(0)}=89.31,\,\!</math> <math>g_{2}^{(0)}=0.127,\,\!</math> <math>g_{3}^{(0)}=0.578\,\!</math>. The iterations are continued to solve for the parameters. Using the RGA software, the estimators of the parameters for the given example are:

:<math>\begin{align}
\widehat{a}&= 0.9299 \\
\widehat{b} &= 0.0943 \\
\widehat{c} &= 0.7170
\end{align}\,\!</math>

The next figure shows the entered data and the estimated parameters.

[[Image:rgaA.1.png|center|600px]]

The Gompertz reliability growth curve may now be written as follows where <math>{{L}_{G}}\,\!</math> is the number of launches, with the first successful launch being counted as <math>{{L}_{G}}=1\,\!</math>. Therefore, <math>{{L}_{G}}\,\!</math> is equal to 19, since reliability growth starts with launch 4.

:<math>R=0.9299{{(0.0943)}^{{{0.7170}^{{{L}_{G}}}}}}\,\!</math>

</li>
<li>The predicted reliability after launch 22 is therefore:

:<math>\begin{align}
R &= 0.9299{{(0.0943)}^{{{0.7170}^{19}}}} \\
&= 0.9260
\end{align}\,\!</math>

The predicted reliability after launch 22 is calculated using the Quick Calculation Pad (QCP), as shown next.

[[Image:rgaA.2.png|center|450px]]

</li>
<li>In the second table, the predicted reliability values are compared with the reliabilities that are calculated from the raw data using failure discounting. It can be seen in the table, and in the following figure, that the Gompertz curve appears to provide a good fit to the actual data.

[[Image:rgaA.3.png|center|450px]]</li>
</ol>

Optimum Overhaul Example

2014-06-12T17:47:15Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Repairable_Systems_Analysis|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

Field data have been collected for a system that begins its wearout phase at time zero. The start time for each system is equal to zero and the end time for each system is 10,000 miles. Each system is scheduled to undergo an overhaul after a certain number of miles. It has been determined that the cost of an overhaul is four times more expensive than a repair. The table below presents the data. Do the following:

#Estimate the parameters of the Power Law model.
#Determine the optimum overhaul interval.
#If <math>\beta <1\,\!</math>, would it be cost-effective to implement an overhaul policy?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"|'''Field Data'''
|-
!System 1
!System 2
!System 3
|-
|1006.3|| 722.7|| 619.1
|-
|2261.2|| 1950.9|| 1519.1
|-
|2367|| 3259.6|| 2956.6
|-
|2615.5|| 4733.9|| 3114.8
|-
|2848.1|| 5105.1|| 3657.9
|-
|4073|| 5624.1|| 4268.9
|-
|5708.1|| 5806.3|| 6690.2
|-
|6464.1|| 5855.6|| 6803.1
|-
|6519.7|| 6325.2|| 7323.9
|-
|6799.1 ||6999.4|| 7501.4
|-
|7342.9 ||7084.4|| 7641.2
|-
|7736 ||7105.9|| 7851.6
|-
|8246.1|| 7290.9|| 8147.6
|-
| || 7614.2|| 8221.9
|-
| || 8332.1|| 9560.5
|-
| || 8368.5|| 9575.4
|-
| || 8947.9||
|-
| || 9012.3 ||
|-
| || 9135.9 ||
|-
| || 9147.5 ||
|-
| || 9601 ||
|}

'''Solution'''
<ol>
<li>The next figure shows the estimated Power Law parameters.

[[Image:rga13.12.png|center|600px]]

</li>
<li>The QCP can be used to calculate the optimum overhaul interval, as shown next.

[[Image:rga13.13.png|center|450px]]

</li>
<li>Since <math>\beta <1\,\!</math> then the systems are not wearing out and it would not be cost-effective to implement an overhaul policy. An overhaul policy makes sense only if the systems are wearing out. Otherwise, an overhauled unit would have the same probability of failing as a unit that was not overhauled.
</li>
</ol>

Auto Transmission Example

2014-06-12T17:46:41Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Repairable_Systems_Analysis|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

This case study is based on the data given in the article "Graphical Analysis of Repair Data" by Dr. Wayne Nelson [[RGA_References|[23]]]. The following table contains repair data on an automatic transmission from a sample of 34 cars. For each car, the data set shows mileage at the time of each transmission repair, along with the latest mileage. The + indicates the latest mileage observed without failure. Car 1, for example, had a repair at 7068 miles and was observed until 26,744 miles. Do the following:

#Estimate the parameters of the Power Law model.
#Estimate the number of warranty claims for a 36,000 mile warranty policy for an estimated fleet of 35,000 vehicles.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="5" style="text-align:center"|'''Automatic Transmission Data'''
|-
!Car
!Mileage
!
!Car
!Mileage
|-
|1|| 7068, 26744+|| || 18|| 17955+
|-
|2|| 28, 13809+|| || 19|| 19507+
|-
|3|| 48, 1440, 29834+|| || 20|| 24177+
|-
|4|| 530, 25660+|| || 21|| 22854+
|-
|5|| 21762+|| || 22|| 17844+
|-
|6|| 14235+|| || 23|| 22637+
|-
|7|| 1388, 18228+|| || 24|| 375, 19607+
|-
|8|| 21401+|| || 25|| 19403+
|-
|9|| 21876+|| || 26|| 20997+
|-
|10|| 5094, 18228+|| || 27|| 19175+
|-
|11|| 21691+|| || 28|| 20425+
|-
|12|| 20890+|| || 29|| 22149+
|-
|13|| 22486+|| || 30|| 21144+
|-
|14|| 19321+|| || 31|| 21237+
|-
|15|| 21585+|| || 32|| 14281+
|-
|16|| 18676+|| || 33|| 8250, 21974+
|-
|17|| 23520+|| || 34|| 19250, 21888+
|}

'''Solution'''
<ol>
<li>The estimated Power Law parameters are shown next.

[[Image:rga13.10.png|center|600px]]
</li>
<li>The expected number of failures at 36,000 miles can be estimated using the QCP as shown next. The model predicts that 0.3559 failures per system will occur by 36,000 miles. This means that for a fleet of 35,000 vehicles, the expected warranty claims are 0.3559 * 35,000 = 12,456.

[[Image:rga13.11.png|center|450px]]
</li>
</ol>

Power Law Model Parameter Estimation Example

2014-06-12T17:45:58Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}{{Navigation box}}
''These examples appear in the [[Repairable_Systems_Analysis|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

For the data in the following table, the starting time for each system is equal to 0 and the ending time for each system is 2,000 hours. Calculate the maximum likelihood estimates <math>\widehat{\lambda }\,\!</math> and <math>\widehat{\beta }\,\!</math>.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"|'''Repairable System Failure Data'''
|-
!System 1 ( <math>{{X}_{i1}}\,\!</math> )
!System 2 ( <math>{{X}_{i2}}\,\!</math> )
!System 3 ( <math>{{X}_{i3}}\,\!</math> )
|-
|1.2|| 1.4|| 0.3
|-
|55.6|| 35.0|| 32.6
|-
|72.7|| 46.8|| 33.4
|-
|111.9|| 65.9|| 241.7
|-
|121.9|| 181.1|| 396.2
|-
|303.6|| 712.6|| 444.4
|-
|326.9|| 1005.7|| 480.8
|-
|1568.4|| 1029.9 ||588.9
|-
|1913.5|| 1675.7|| 1043.9
|-
| ||1787.5|| 1136.1
|-
| ||1867.0|| 1288.1
|-
| || ||1408.1
|-
| || ||1439.4
|-
| || ||1604.8
|-
|<math>{{N}_{1}}=9\,\!</math> || <math>{{N}_{2}}=11\,\!</math> ||<math>{{N}_{3}}=14\,\!</math>
|}

'''Solution'''

Because the starting time for each system is equal to zero and each system has an equivalent ending time, the general equations for <math>\widehat{\beta }\,\!</math> and <math>\widehat{\lambda }\,\!</math> reduce to the closed form equations. The maximum likelihood estimates of <math>\hat{\beta }\,\!</math> and <math>\hat{\lambda }\,\!</math> are then calculated as follows:

:<math>\widehat{\beta }= \frac{\underset{q=1}{\overset{K}{\mathop{\sum }}}\,{{N}_{q}}}{\underset{q=1}{\overset{K}{\mathop{\sum }}}\,\underset{i=1}{\overset{{{N}_{q}}}{\mathop{\sum }}}\,\ln (\tfrac{T}{{{X}_{iq}}})} = 0.45300 </math>

:<math>\widehat{\lambda }= \frac{\underset{q=1}{\overset{K}{\mathop{\sum }}}\,{{N}_{q}}}{K{{T}^{\beta }}} = 0.36224 \,\!</math>

The system failure intensity function is then estimated by:

:<math>\widehat{u}(t)=\widehat{\lambda }\widehat{\beta }{{t}^{\widehat{\beta }-1}},\text{ }t>0\,\!</math>

The next figure is a plot of <math>\widehat{u}(t)\,\!</math> over the period (0, 3000). Clearly, the estimated failure intensity function is most representative over the range of the data and any extrapolation should be viewed with the usual caution.

[[File:Instantaneous Failure Intensity vs. Time plot.png|450px|center]]

Lloyd-Lipow Least Squares Example

2014-06-12T17:41:35Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Lloyd-Lipow|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

After a 20-stage reliability development test program, 20 groups of success/failure data were obtained and are given in the table below. Do the following:

#Fit the Lloyd-Lipow model to the data using least squares.
#Plot the reliabilities predicted by the Lloyd-Lipow model along with the observed reliabilities, and compare the results.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''The Test Results and Reliabilities of Each Stage Calculated from Raw Data and the Predicted Reliability'''
!Test Stage Number(<math>k\,\!</math>)
!Number of Tests in Stage(<math>n_k\,\!</math>)
!Number of Successful Tests(<math>S_k\,\!</math>)
!Raw Data Reliability
!Lloyd-Lipow Reliability
|-
|1|| 9|| 6|| 0.667|| 0.7002
|-
|2|| 9|| 5|| 0.556|| 0.7369
|-
|3|| 8|| 7|| 0.875|| 0.7552
|-
|4|| 10|| 6|| 0.600|| 0.7662
|-
|5|| 9|| 7|| 0.778|| 0.7736
|-
|
|-
|6|| 10|| 8|| 0.800|| 0.7788
|-
|7|| 10|| 7|| 0.700|| 0.7827
|-
|8|| 10|| 6|| 0.600|| 0.7858
|-
|9|| 11|| 7|| 0.636|| 0.7882
|-
|10|| 11|| 9|| 0.818|| 0.7902
|-
|
|-
|11|| 9|| 9|| 1.000|| 0.7919
|-
|12|| 12|| 10|| 0.833|| 0.7933
|-
|13|| 12|| 9|| 0.750|| 0.7945
|-
|14|| 11|| 8|| 0.727|| 0.7956
|-
|15|| 10|| 7|| 0.700|| 0.7965
|-
|
|-
|16|| 10|| 8|| 0.800|| 0.7973
|-
|17|| 11|| 10|| 0.909|| 0.7980
|-
|18|| 10|| 9|| 0.900|| 0.7987
|-
|19|| 9|| 8|| 0.889|| 0.7992
|-
|20|| 8|| 7|| 0.875|| 0.7998
|}

'''Solution'''
<ol>
<li>The least squares estimates are:

:<math>\begin{align}
\underset{k=1}{\overset{N}{\mathop \sum }}\,\frac{1}{k}= & \underset{k=1}{\overset{20}{\mathop \sum }}\,\frac{1}{k}=3.5977 \\
\underset{k=1}{\overset{N}{\mathop \sum }}\,\frac{1}{{{k}^{2}}}= & \underset{k=1}{\overset{20}{\mathop \sum }}\,\frac{1}{{{k}^{2}}}=1.5962 \\
\underset{k=1}{\overset{N}{\mathop \sum }}\,\frac{{{S}_{k}}}{{{n}_{k}}}= & \underset{k=1}{\overset{20}{\mathop \sum }}\,\frac{{{S}_{k}}}{{{n}_{k}}}=15.4131
\end{align}\,\!</math>

and:

:<math>\underset{k=1}{\overset{N}{\mathop \sum }}\,\frac{{{S}_{k}}}{k\cdot {{n}_{k}}}=\underset{k=1}{\overset{20}{\mathop \sum }}\,\frac{{{S}_{k}}}{k\cdot {{n}_{k}}}=2.5632\,\!</math>

Using these estimates to obtain <math>\hat{R_{\infty}}\,\!</math> and <math>\hat{\alpha}\,\!</math>yields:

:<math>\begin{align}
\text{ }{{\hat{R}}_{\infty }}= &\frac{\underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{1}{{{k}^{2}}}\underset{k=1}{\overset{N}{\mathop{\sum }}}\,{{R}_{k}}-\underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{1}{k}\underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{{{R}_{k}}}{k}}{N\underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{1}{{{k}^{2}}}-{{\left( \underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{1}{k} \right)}^{2}}} \\

= & \frac{(1.5962)(15.413)-(3.5977)(2.5637)}{(20)(1.5962)-{{(3.5977)}^{2}}} \\
= & 0.8104
\end{align}\,\!</math>

and:

:<math>\begin{align}
\hat{\alpha }= &\frac{\underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{1}{k}\underset{k=1}{\overset{N}{\mathop{\sum }}}\,{{R}_{k}}-N\underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{{{R}_{k}}}{k}}{N\underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{1}{{{k}^{2}}}-{{\left( \underset{k=1}{\overset{N}{\mathop{\sum }}}\,\tfrac{1}{k} \right)}^{2}}}\\
= & \frac{(3.5977)(15.413)-(20)(2.5637)}{(20)(1.5962)-{{(3.5977)}^{2}}} \\
= & 0.2207
\end{align}\,\!</math>

Therefore, the Lloyd-Lipow reliability growth model is as follows, where <math>k\,\!</math> is the test stage.

:<math>{{R}_{k}}=0.8104-\frac{0.2201}{k}\,\!</math>
</li>
<li>The reliabilities from the raw data and the reliabilities predicted from the Lloyd-Lipow reliability growth model are given in the last two columns of the table. The figure below shows the plot. Based on the given data, the model cannot do much more than to basically fit a line through the middle of the points.

[[Image:rga6.1.png|center|450px]]

</li>
</ol>

Sequential Data with Failure Modes - Logistic Model

2014-06-12T17:22:39Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Logistic|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

Consider the data given <noinclude>in the [[Logistic_Model_-_Missile_Launch_Test_Example|Missile Launch Test]] example</noinclude><includeonly>in the previous example</includeonly>. Now suppose that the engineers assigned failure modes to each failure and that the appropriate corrective actions were taken.

The table below presents the data.
#Find the Logistic reliability growth curve that best represents the data.
#Plot it comparatively with the raw data.
#If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99.50% be achieved?
#If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of the 35th launch?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Sequential Success/Failure Data with Modes'''
!Launch Number
!Result
!Mode
|-
|1|| F|| 2
|-
|2|| F|| 1
|-
|3|| S||
|-
|4|| F|| 3
|-
|5|| F|| 3
|-
|6|| S||
|-
|7|| S||
|-
|8|| S||
|-
|9|| F|| 2
|-
|10|| S||
|-
|11|| F|| 1
|-
|12|| S||
|-
|13|| S||
|-
|14|| S||
|-
|15|| S||
|-
|16|| S||
|-
|17|| S||
|-
|18|| S||
|-
|19|| S||
|-
|20|| S||
|}

'''Solution'''
<ol>
<li>The next figure shows the entered data and the estimated parameters.
 
[[Image:rga8.15.png|center|650px|Entered data and the estimated Logistic parameters.]]
 </li>
<li>The next figure displays the Reliability vs. Time plot.
 
[[Image:rga8.16.png|center|400px|Reliability vs. Time plot.]]
 </li>
<li>The next figure displays the number of launches before the reliability goal of 99.5% will be achieved.
 
[[Image:rga8.17.png|center|400px|Calculate when the reliability goal of 99.5% will be achieved.]]
 </li>
<li>The last figure displays the reliability after the 35th launch.
 
[[Image:rga8.18.png|center|400px|Calculate the reliability at the end of the 35th launch.]]
</li>
</ol>

Logistic Model - Missile Launch Test Example

2014-06-12T17:22:14Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Logistic|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

The following table presents the results for a missile launch test. The test consisted of 20 attempts. If the missile launched, it was recorded as a success. If not, it was recorded as a failure. Note that, at this development stage, the test did not consider whether or not the target was destroyed.

#Find a Logistic reliability growth curve that best represents the data.
#Plot it comparatively with the raw data.
#If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99.5% with a 90% confidence level be achieved?
#If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of the 35th launch?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Sequential Success/Failure Data'''
!Launch Number
!Result
|-
|1|| F
|-
|2|| F
|-
|3|| S
|-
|4|| F
|-
|5|| F
|-
|6|| S
|-
|7|| S
|-
|8|| S
|-
|9|| F
|-
|10|| S
|-
|11|| F
|-
|12|| S
|-
|13|| S
|-
|14|| S
|-
|15|| S
|-
|16|| S
|-
|17|| S
|-
|18|| S
|-
|19|| S
|-
|20|| S
|}

'''Solution'''
<ol>
<li>The next figure shows the entered data and the estimated parameters.
 
[[Image:rga8.11.png|center|650px|Entered data and the estimated logistic parameters.]]</li>
<li>The next figure displays the Reliability vs. Time plot.
 
[[Image:rga8.12.png|center|400px|Reliability vs. Time plot.]]</li>
<li>The next figure displays the number of launches before the reliability goal of 99.5% will be achieved with a 90% confidence level.
 
[[Image:rga8.13.png|center|400px|When the reliability goal of 99.5% with a 90% confidence level will be achieved.]]</li>
<li>The next figure displays the reliability achieved after the 35th launch.
 
[[Image:rga8.14.png|center|400px|The reliability at the end of the 35th launch.]]</li>
</ol>

Logistic Model - Missile Launch Test Example

2014-06-12T17:22:02Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Logistic|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

The following table presents the results for a missile launch test. The test consisted of 20 attempts. If the missile launched, it was recorded as a success. If not, it was recorded as a failure. Note that, at this development stage, the test did not consider whether or not the target was destroyed.

#Find a Logistic reliability growth curve that best represents the data.
#Plot it comparatively with the raw data.
#If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99.5% with a 90% confidence level be achieved?
#If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of the 35th launch?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Sequential Success/Failure Data'''
!Launch Number
!Result
|-
|1|| F
|-
|2|| F
|-
|3|| S
|-
|4|| F
|-
|5|| F
|-
|6|| S
|-
|7|| S
|-
|8|| S
|-
|9|| F
|-
|10|| S
|-
|11|| F
|-
|12|| S
|-
|13|| S
|-
|14|| S
|-
|15|| S
|-
|16|| S
|-
|17|| S
|-
|18|| S
|-
|19|| S
|-
|20|| S
|}

'''Solution'''
<ol>
<li>The next figure shows the entered data and the estimated parameters.
 
[[Image:rga8.11.png|center|650px|Entered data and the estimated logistic parameters.]]</li>
<li>The next figure displays the Reliability vs. Time plot.
 
[[Image:rga8.12.png|center|400px|Reliability vs. Time plot.]]</li>
<li>The next figure displays the number of launches before the reliability goal of 99.5% will be achieved with a 90% confidence level.
 
[[Image:rga8.13.png|thumb|center|400px|When the reliability goal of 99.5% with a 90% confidence level will be achieved.]]</li>
<li>The next figure displays the reliability achieved after the 35th launch.
 
[[Image:rga8.14.png|center|400px|The reliability at the end of the 35th launch.]]</li>
</ol>

Logistic Model - Auto Transmission Example

2014-06-12T17:04:25Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Logistic|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

The following table presents the reliabilities observed monthly for an automobile transmission that was tested for one year.

#Find a Logistic reliability growth curve that best represents the data.
#Plot it comparatively with the raw data.
#If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99% be achieved?
#If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of January the following year?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Reliability Data'''
!Month
!Observed Reliability(%)
|-
|June|| 22
|-
|July|| 26
|-
|August|| 30
|-
|September|| 34
|-
|October|| 45
|-
|November|| 58
|-
|December|| 68
|-
|January|| 79
|-
|February|| 85
|-
|March|| 89
|-
|April|| 92
|-
|May|| 95
|}

'''Solution '''
<ol>
<li>The next figure shows the entered data and the estimated parameters.
 
[[Image:rga8.7.png|center|650px|Entered data and the estimated Logistic parameters.]]
 
</li>
<li>The next figure displays the Reliability vs. Time plot.
 
[[Image:rga8.8.png|center|400px|Reliability vs. Time plot.]]
 
</li>
<li>Using the QCP, the next figure displays, in months, when the reliability goal of 99% will be achieved.
 
[[Image:rga8.9.png|center|400px|When the reliability goal of 99% will be achieved.]]
 
</li>
<li>The last figure shows the reliability at the end of January the following year (i.e., after 20 months of testing and development).
 
[[Image:rga8.10.png|center|400px|The reliability at the end of the following January (month=20)]]
 
</li>
</ol>

Sequential Data with Failure Modes - Logistic Model

2014-06-12T17:02:13Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Logistic|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

Consider the data given <noinclude>in the [[Logistic_Model_-_Missile_Launch_Test_Example|Missile Launch Test]] example</noinclude><includeonly>in the previous example</includeonly>. Now suppose that the engineers assigned failure modes to each failure and that the appropriate corrective actions were taken.

The table below presents the data.
#Find the Logistic reliability growth curve that best represents the data.
#Plot it comparatively with the raw data.
#If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99.50% be achieved?
#If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of the 35th launch?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Sequential Success/Failure Data with Modes'''
!Launch Number
!Result
!Mode
|-
|1|| F|| 2
|-
|2|| F|| 1
|-
|3|| S||
|-
|4|| F|| 3
|-
|5|| F|| 3
|-
|6|| S||
|-
|7|| S||
|-
|8|| S||
|-
|9|| F|| 2
|-
|10|| S||
|-
|11|| F|| 1
|-
|12|| S||
|-
|13|| S||
|-
|14|| S||
|-
|15|| S||
|-
|16|| S||
|-
|17|| S||
|-
|18|| S||
|-
|19|| S||
|-
|20|| S||
|}

'''Solution'''
<ol>
<li>The next figure shows the entered data and the estimated parameters.
 
[[Image:rga8.15.png|center|650px|Entered data and the estimated Logistic parameters.]]
 </li>
<li>The next figure displays the Reliability vs. Time plot.
 
[[Image:rga8.16.png|center|400px|Reliability vs. Time plot.]]
 </li>
<li>The next figure displays the launch when the reliability goal of 99.5% will be achieved.
 
[[Image:rga8.17.png|center|400px|Calculate when the reliability goal of 99.5% will be achieved.]]
 </li>
<li>The last figure displays the reliability after the 35th launch.
 
[[Image:rga8.18.png|center|400px|Calculate the reliability at the end of the 35th launch.]]
</li>
</ol>

Sequential Data with Failure Modes - Logistic Model

2014-06-12T16:54:09Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Logistic|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

Consider the data given <noinclude>in the [[Logistic_Model_-_Missile_Launch_Test_Example|Missile Launch Test]] example</noinclude><includeonly>in the previous example</includeonly>. Now suppose that the engineers assigned failure modes to each failure and that the appropriate corrective actions were taken.

The table below presents the data.
#Find the Logistic reliability growth curve that best represents the data.
#Plot it comparatively with the raw data.
#If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99.50% be achieved?
#If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of the 35th launch?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Sequential Success/Failure Data with Modes'''
!Launch Number
!Result
!Mode
|-
|1|| F|| 2
|-
|2|| F|| 1
|-
|3|| S||
|-
|4|| F|| 3
|-
|5|| F|| 3
|-
|6|| S||
|-
|7|| S||
|-
|8|| S||
|-
|9|| F|| 2
|-
|10|| S||
|-
|11|| F|| 1
|-
|12|| S||
|-
|13|| S||
|-
|14|| S||
|-
|15|| S||
|-
|16|| S||
|-
|17|| S||
|-
|18|| S||
|-
|19|| S||
|-
|20|| S||
|}

'''Solution'''
<ol>
<li>The next figure shows the estimated parameters.
 
[[Image:rga8.15.png|thumb|center|650px|Entered data and the estimated Logistic parameters.]]
 </li>
<li>The next figure displays the Reliability vs. Time plot.
 
[[Image:rga8.16.png|thumb|center|400px|Reliability vs. Time plot.]]
 </li>
<li>The next figure displays when the reliability goal of 99.5% will be achieved.
 
[[Image:rga8.17.png|thumb|center|400px|Calculate when the reliability goal of 99.5% will be achieved.]]
 </li>
<li>The last figure displays the reliability after the 35th launch.
 
[[Image:rga8.18.png|thumb|center|400px|Calculate the reliability at the end of the 35th launch.]]
</li>
</ol>

Logistic Model - Missile Launch Test Example

2014-06-12T16:52:41Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Logistic|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

The following table presents the results for a missile launch test. The test consisted of 20 attempts. If the missile launched, it was recorded as a success. If not, it was recorded as a failure. Note that, at this development stage, the test did not consider whether or not the target was destroyed.

#Find a Logistic reliability growth curve that best represents the data.
#Plot it comparatively with the raw data.
#If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99.5% with a 90% confidence level be achieved?
#If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of the 35th launch?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Sequential Success/Failure Data'''
!Launch Number
!Result
|-
|1|| F
|-
|2|| F
|-
|3|| S
|-
|4|| F
|-
|5|| F
|-
|6|| S
|-
|7|| S
|-
|8|| S
|-
|9|| F
|-
|10|| S
|-
|11|| F
|-
|12|| S
|-
|13|| S
|-
|14|| S
|-
|15|| S
|-
|16|| S
|-
|17|| S
|-
|18|| S
|-
|19|| S
|-
|20|| S
|}

'''Solution'''
<ol>
<li>The next figure shows the entered data and the estimated parameters.
 
[[Image:rga8.11.png|thumb|center|650px|Entered data and the estimated logistic parameters.]]</li>
<li>The next figure displays the Reliability vs. Time plot.
 
[[Image:rga8.12.png|thumb|center|400px|Reliability vs. Time plot.]]</li>
<li>The next figure displays when the reliability goal of 99.5% will be achieved with a 90% confidence level.
 
[[Image:rga8.13.png|thumb|center|400px|When the reliability goal of 99.5% with a 90% confidence level will be achieved.]]</li>
<li>The next figure displays the reliability achieved after the 35th launch.
 
[[Image:rga8.14.png|thumb|center|400px|The reliability at the end of the 35th launch.]]</li>
</ol>

Logistic Model - Auto Transmission Example

2014-06-12T16:51:29Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Logistic|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

The following table presents the reliabilities observed monthly for an automobile transmission that was tested for one year.

#Find a Logistic reliability growth curve that best represents the data.
#Plot it comparatively with the raw data.
#If design changes continue to be incorporated and the testing continues, when will the reliability goal of 99% be achieved?
#If design changes continue to be incorporated and the testing continues, what will be the attainable reliability at the end of January the following year?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Reliability Data'''
!Month
!Observed Reliability(%)
|-
|June|| 22
|-
|July|| 26
|-
|August|| 30
|-
|September|| 34
|-
|October|| 45
|-
|November|| 58
|-
|December|| 68
|-
|January|| 79
|-
|February|| 85
|-
|March|| 89
|-
|April|| 92
|-
|May|| 95
|}

'''Solution '''
<ol>
<li>The next figure shows the estimated parameters.
 
[[Image:rga8.7.png|thumb|center|650px|Entered data and the estimated Logistic parameters.]]
 
</li>
<li>The next figure displays the Reliability vs. Time plot.
 
[[Image:rga8.8.png|thumb|center|400px|Reliability vs. Time plot.]]
 
</li>
<li>Using the QCP, the next figure displays when the reliability goal of 99% will be achieved.
 
[[Image:rga8.9.png|thumb|center|400px|When the reliability goal of 99% will be achieved.]]
 
</li>
<li>The last figure shows the reliability at the end of January the following year (i.e., after 20 months of testing and development).
 
[[Image:rga8.10.png|thumb|center|400px|The reliability at the end of the following January (month=20)]]
 
</li>
</ol>

Operational Mission Profile Testing

2014-06-12T16:22:10Z

Chris Kahn:

{{template:RGA BOOK|5|Operational Mission Profile Testing}}
It is common practice for systems to be subjected to operational testing during a development program. The objective of this testing is to evaluate the performance of the system, including reliability, under conditions that represent actual use. Because of budget, resources, schedule and other considerations, these operational tests rarely match exactly the actual use conditions. Usually, stated mission profile conditions are used for operational testing. These mission profile conditions are typically general statements that guide testing on an average basis. For example, a copier might be required to print 3,000 pages by time T=10 days and 5,000 pages by time T=15 days. In addition the copier is required to scan 200 documents by time T=10 days, 250 documents by time T=15 days, etc.

Because of practical constraints, these full mission profile conditions are typically not repeated one after the other during testing. Instead, the elements that make up the mission profile conditions are tested under varying schedules with the intent that, on average, the mission profile conditions are met. In practice, reliability corrective actions are generally incorporated into the system as a result of this type of testing.

Because of a lack of structure for managing the elements that make up the mission profile, it is difficult to have an agreed upon methodology for estimating the system's reliability. Many systems fail operational testing because key assessments such as growth potential and projections cannot be made in a straightforward manner so that management can take appropriate action. The RGA software addresses this issue by incorporating a systematic mission profile methodology for operational reliability testing and reliability growth assessments.

==Introduction==
Operational testing is an attempt to subject the system to conditions close to the actual environment that is expected under customer use. Often this is an extension of reliability growth testing where operation induced failure modes and corrective actions are of prime interest. Sometimes the stated intent is for a demonstration test where corrective actions are not the prime objective. However, it is not unusual for a system to fail the demonstration test, and the management issue is what to do next. In both cases, important and valid key parameters are needed to properly assess this situation and make cost-effective and timely decisions. This is often difficult in practice.

For example, a system may be required to:
* Conduct a specific task a fixed number times for each hour of operation (task 1).
* Move a fixed number of miles under a specific operating condition for each hour of operation (task 2).
* Move a fixed number of miles under another operating condition for each hour of operation (task 3).

During operational testing, these guidelines are met individually as averages. For example, the actual as-tested profile for task 1 may not be uniform relative to the stated mission guidelines during the testing. What is often the case is that some of the tasks (for example task 1) could be operated below the stated guidelines. This can mask a major reliability problem. In other cases during testing, tasks 1, 2 and 3 might never meet their stated averages, except perhaps at the end of the test. This becomes an issue because an important aspect of effective reliability risk management is to not wait until the end of the test to have an assessment of the reliability performance.

Because the elements of the mission profile during the testing will rarely, if ever, balance continuously to the stated averages, a common analysis method is to piece the reliability assessments together by evaluating each element of the profile separately. This is not a well-defined methodology and does not account for improvement during the testing. It is therefore not unusual for two separate organizations (e.g., the customer and the developer) to analyze the same data and obtain different MTBF numbers. In addition, this method does not address the delayed corrective actions that are to be incorporated at the end of the test nor does it estimate growth potential or interaction effects. Therefore, to reduce this risk there is a need for a rigorous methodology for reliability during operational testing that does not rely on piecewise analysis and avoids the issues noted above.

The RGA software incorporates a new methodology to manage system reliability during operational mission profile testing. This methodology draws information from particular plots of the operational test data and inserts key information into a growth model. The improved methodology does not piece the analysis together, but gives a direct MTBF mission profile estimate of the system's reliability that is directly compared to the MTBF requirement. The methodology will reflect any reliability growth improvement during the test, and will also give management a higher projected MTBF for the system mission profile reliability after delayed corrected actions are incorporated at the end of the test. In addition, the methodology also gives an estimate of the system's growth potential, and provides management metrics to evaluate whether changes in the program need to be made. A key advantage is that the methodology is well-defined and all organizations will arrive at the same reliability assessment with the same data.

==Testing Methodology==
The methodology described here will use the [[Crow Extended|Crow extended model]] for data analysis. In order to have valid Crow extended model assessments, it is required that the operational mission profile be conducted in a structured manner. Therefore, this testing methodology involves convergence and stopping points during the testing. A stopping point is when the testing is stopped for the expressed purpose of incorporating the type BD delayed corrective actions. There may be more than one stopping point during a particular testing phase. For simplicity, the methodology with only one stopping point will be described; however, the methodology can be extended to the case of more than one stopping point. A convergence point is a time during the test when all the operational mission profile tasks meet their expected averages or fall within an acceptable range. At least three convergence points are required for a well-balanced test. The end of the test, time <math>T\,\!</math>, must be a convergence point. The test times between the convergence points do not have to be the same.
 

The objective of having the convergence points is to be able to apply the Crow extended model directly in such a way that the projection and other key reliability growth parameters can be estimated in a valid fashion. To do this, the grouped data methodology is applied. Note that the methodology can also be used with the Crow-AMSAA (NHPP) model for a simpler analysis without the ability to estimate projected and growth potential reliability. See the [[Crow-AMSAA (NHPP)#Grouped_Data|Grouped Data for the Crow-AMSAA (NHPP) model]] or for the [[Crow_Extended#Grouped_Data|Crow extended model]].

==Example - Mission Profile Testing==
Consider the test-fix-find-test data set that was introduced in the [[Crow_Extended#Example_-_Test-Fix-Find-Test_Data|Crow Extended model chapter]] and is shown again in the table below. The total test time for this test is 400 hours. Note that for this example we assume one stopping point at the end of the test for the incorporation of the delayed fixes. Also, suppose that the data set represents a military system with:

* Task 1 = firing a gun.
* Task 2 = moving under environment E1.
* Task 3 = moving under environment E2.

For every hour of operation, the operational profile states that the system operates in the E1 environment for 70% of the time and in the E2 environment for 30% of the time. In addition, for each hour of operation, the gun must be fired 10 times.

{{Text-Fix-Find-Test Data}}

In general, it is difficult to manage an operational test so that these operational profiles are continuously met throughout the test. However, the operational mission profile methodology requires that these conditions be met on average at the convergence points. In practice, this almost always can be done with proper program and test management. The convergence points are set for the testing, often at interim assessment points. The process for controlling the convergence at these points involves monitoring a graph for each of the tasks.

The following table shows the expected and actual results for each of the operational mission profiles.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"

|colspan="7" style="text-align:center"|'''Expected and Actual Results for Profiles 1, 2, 3'''
|-
| ||colspan="2" style="text-align: center;" | Profile 1(gun firings)|| colspan="2" style="text-align: center;" | Profile 2(E1)|| colspan="2" style="text-align: center;" | Profile 3(E2)
|-
|Time||Expected||Actual||Expected||Actual||Expected||Actual
|-
|5|| 50|| 0|| 3.5|| 5|| 1.5|| 0
|-
|10|| 100|| 0|| 7|| 10|| 3|| 0
|-
|15|| 150|| 0|| 10.5|| 15|| 4.5|| 0
|-
|20|| 200|| 0|| 14|| 20|| 6|| 0
|-
|25|| 250|| 100|| 17.5|| 25|| 7.5|| 0
|-
|30|| 300|| 150|| 21|| 30|| 9|| 0
|-
|35|| 350|| 400|| 24.5|| 30|| 10.5|| 5
|-
|40|| 400|| 600|| 28|| 30|| 12|| 10
|-
|45|| 450|| 600|| 31.5|| 30|| 13.5|| 15
|-
|50|| 500|| 600|| 35|| 30|| 15|| 20
|-
|55|| 550|| 800|| 38.5|| 35|| 16.5|| 20
|-
|60|| 600|| 800|| 42|| 40|| 18|| 20
|-
|65|| 650|| 800|| 45.5|| 45|| 19.5|| 20
|-
|70|| 700|| 800|| 49|| 50|| 21|| 20
|-
|75|| 750|| 800|| 52.5|| 55|| 22.5|| 20
|-
|80|| 800|| 900|| 56|| 55|| 24|| 25
|-
|85|| 850|| 950|| 59.5|| 55|| 25.5|| 30
|-
|90|| 900|| 1000|| 63|| 60|| 27|| 30
|-
|95|| 950|| 1000|| 66.5|| 65|| 28.5|| 30
|-
|100|| 1000|| 1000|| 70|| 70|| 30|| 30
|-
|105|| 1050|| 1000|| 73.5|| 70|| 31.5|| 35
|-
|...||...||...||...||...||...||
|-
|...||...||...||...||...||...||
|-
|355|| 3550|| 3440|| 248.5|| 259|| 106.5|| 96
|-
|360|| 3600|| 3690|| 252|| 264|| 108|| 96
|-
|365|| 3650|| 3690|| 255.5|| 269|| 109.5|| 96
|-
|370|| 3700|| 3850|| 259|| 274|| 111|| 96
|-
|375|| 3750|| 3850|| 262.5|| 279|| 112.5|| 96
|-
|380|| 3800|| 3850|| 266|| 280|| 114|| 100
|-
|385|| 3850|| 3850|| 269.5|| 280|| 115.5|| 105
|-
|390|| 3900|| 3850|| 273|| 280|| 117|| 110
|-
|395|| 3950|| 4000|| 276.5|| 280|| 118.5|| 115
|-
|400|| 4000|| 4000|| 280|| 280|| 120|| 120
|}

The next figure shows a portion of the expected and actual results for mission profile 1, as entered in the RGA software.

[[Image:rga12.1.png|center|450px]]

A graph exists for each of the three tasks in this example. Each graph has a line with the expected average as a function of hours, and the corresponding actual value. When the actual value for a task meets the expected value then it is a convergence for that task. A convergence point occurs when all of the tasks converge at the same time. At least three convergence points are required, one of which is the stopping point <math>T\,\!</math>. In our example, the total test time is 400 hours. The convergence points were chosen to be at 100, 250, 320 and 400 hours. The next figure shows the data sheet that contains the convergence points in the RGA software.

[[Image:rga12.2.png|center|450px]]

The testing profiles are managed so that at these times the actual operational test profile equals the expected values for the three tasks or falls within an acceptable range. The next graph shows the expected and actual gun firings.

[[Image:rga12.3.png|center|450px]]

While the next two graphs show the expected and actual time in environments E1 and E2, respectively.

[[Image:rga12.4.png|center|450px]]

[[Image:rga12.5.png|center|450px]]

The objective of having the convergence points is to be able to apply the Crow extended model directly in such a way that the projection and other key reliability growth parameters can be estimated in a valid fashion. To do this, grouped data is applied using the Crow extended model. For reliability growth assessments using grouped data, only the information between time points in the testing is used. In our application, these time points are the convergence points 100, 250, 320, and 400. The next figure shows all three mission profiles plotted in the same graph, together with the convergence points.

[[Image:rga12.6.png|center|450px]]

The following table gives the grouped data input corresponding to the original data set.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="9" style="text-align:center"|'''Grouped Data at Convergence Points 100, 250, 320 and 400 Hours'''
|-
!Number at Event
!Time to Event
!Classification
!Mode
!
!Number at Event
!Time to Event
!Classification
!Mode
|-
|3|| 100|| BC|| 17|| || 1|| 250|| BC|| 26
|-
|1|| 100|| BD|| 1|| || 1|| 250|| BD|| 11
|-
|1|| 100|| BC|| 18|| || 1|| 250|| BD|| 12
|-
|1|| 100|| BD|| 2|| || 3|| 320|| A||
|-
|1|| 100|| BD|| 3|| || 1|| 320|| BD|| 1
|-
|1|| 100|| BD|| 4|| || 1|| 320|| BD|| 8
|-
|1|| 100|| BC|| 19|| || 1|| 320|| BD|| 6
|-
|2|| 100|| BD|| 5|| || 1|| 320|| BC|| 27
|-
|1|| 100|| A|| || || 1|| 320|| BD|| 13
|-
|1|| 100|| BC|| 20|| || 1|| 320|| BD|| 9
|-
|1|| 100|| BD|| 6|| || 1|| 320|| BD|| 4
|-
|1|| 250|| BD|| 7|| || 3|| 400|| A||
|-
|3|| 250|| A|| || || 1|| 400|| BD|| 12
|-
|1|| 250|| BD|| 8|| || 2|| 400|| BD|| 10
|-
|1|| 250|| BC|| 21|| || 1|| 400|| BD|| 5
|-
|1|| 250|| BD|| 2|| || 1|| 400|| BD|| 3
|-
|1|| 250|| BC|| 22|| || 1|| 400|| BC|| 28
|-
|2|| 250|| BD|| 9|| || 1|| 400|| BD|| 2
|-
|2|| 250|| BD|| 10|| || 1|| 400|| BD|| 8
|-
|1|| 250|| BC|| 23|| || 1|| 400|| BD|| 14
|-
|1|| 250|| BC|| 24|| || 1|| 400|| BD|| 15
|-
|1|| 250|| BC|| 25|| || 1|| 400|| BD|| 16
|}

The parameters of the Crow extended model for grouped data are then estimated, as explained in the Grouped Data section of the [[Crow_Extended#Grouped_Data|Crow Extended]] chapter. The following table shows the effectiveness factors (EFs) for the BD modes.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Effectiveness Factors for Delayed Fixes'''
|-
!Mode
!Effectiveness Factor
|-
|1|| 0.67
|-
|2|| 0.72
|-
|3|| 0.77
|-
|4|| 0.77
|-
|5|| 0.87
|-
|6|| 0.92
|-
|7|| 0.50
|-
|8|| 0.85
|-
|9|| 0.89
|-
|10|| 0.74
|-
|11|| 0.70
|-
|12|| 0.63
|-
|13|| 0.64
|-
|14|| 0.72
|-
|15|| 0.69
|-
|16|| 0.46
|}

Using the failure times data sheet shown next, we can analyze this data set based on a specified mission profile. This will group the failure times data into groups based on the convergence points that have already been specified when constructing the mission profile.

[[Image:rga12.7.png|center|600px]]

A new data sheet with the grouped data is created, as shown in the figure below and the calculated results based on the grouped data are as follows:

[[Image:rga12.9.png|center|600px]]

The following plot shows the instantaneous, demonstrated, projected and growth potential MTBF for the grouped data, based the mission profile grouping with intervals at the specified convergence points of the mission profile.

[[Image:rga12.10.png|center|450px]]

{{Examples Box|RGA Examples|More mission profile examples are available! See also:
{{Examples Link External|http://www.reliasoft.com/rga/examples/rgex7/index.htm|Mission Profile Testing}}<nowiki/>
}}

Operational Mission Profile Testing

2014-06-12T16:21:17Z

Chris Kahn: /* Example - Mission Profile Testing */

{{template:RGA BOOK|5|Operational Mission Profile Testing}}
It is common practice for systems to be subjected to operational testing during a development program. The objective of this testing is to evaluate the performance of the system, including reliability, under conditions that represent actual use. Because of budget, resources, schedule and other considerations, these operational tests rarely match exactly the actual use conditions. Usually, stated mission profile conditions are used for operational testing. These mission profile conditions are typically general statements that guide testing on an average basis. For example, a copier might be required to print 3,000 pages by time T=10 days and 5,000 pages by time T=15 days. In addition the copier is required to scan 200 documents by time T=10 days, 250 documents by time T=15 days, etc.

Because of practical constraints, these full mission profile conditions are typically not repeated one after the other during testing. Instead, the elements that make up the mission profile conditions are tested under varying schedules with the intent that, on average, the mission profile conditions are met. In practice, reliability corrective actions are generally incorporated into the system as a result of this type of testing.

Because of a lack of structure for managing the elements that make up the mission profile, it is difficult to have an agreed upon methodology for estimating the system's reliability. Many systems fail operational testing because key assessments such as growth potential and projections cannot be made in a straightforward manner so that management can take appropriate action. The RGA software addresses this issue by incorporating a systematic mission profile methodology for operational reliability testing and reliability growth assessments.

==Introduction==
Operational testing is an attempt to subject the system to conditions close to the actual environment that is expected under customer use. Often this is an extension of reliability growth testing where operation induced failure modes and corrective actions are of prime interest. Sometimes the stated intent is for a demonstration test where corrective actions are not the prime objective. However, it is not unusual for a system to fail the demonstration test, and the management issue is what to do next. In both cases, important and valid key parameters are needed to properly assess this situation and make cost-effective and timely decisions. This is often difficult in practice.

For example, a system may be required to:
* Conduct a specific task a fixed number times for each hour of operation (task 1).
* Move a fixed number of miles under a specific operating condition for each hour of operation (task 2).
* Move a fixed number of miles under another operating condition for each hour of operation (task 3).

During operational testing, these guidelines are met individually as averages. For example, the actual as-tested profile for task 1 may not be uniform relative to the stated mission guidelines during the testing. What is often the case is that some of the tasks (for example task 1) could be operated below the stated guidelines. This can mask a major reliability problem. In other cases during testing, tasks 1, 2 and 3 might never meet their stated averages, except perhaps at the end of the test. This becomes an issue because an important aspect of effective reliability risk management is to not wait until the end of the test to have an assessment of the reliability performance.

Because the elements of the mission profile during the testing will rarely, if ever, balance continuously to the stated averages, a common analysis method is to piece the reliability assessments together by evaluating each element of the profile separately. This is not a well-defined methodology and does not account for improvement during the testing. It is therefore not unusual for two separate organizations (e.g., the customer and the developer) to analyze the same data and obtain different MTBF numbers. In addition, this method does not address the delayed corrective actions that are to be incorporated at the end of the test nor does it estimate growth potential or interaction effects. Therefore, to reduce this risk there is a need for a rigorous methodology for reliability during operational testing that does not rely on piecewise analysis and avoids the issues noted above.

The RGA software incorporates a new methodology to manage system reliability during operational mission profile testing. This methodology draws information from particular plots of the operational test data and inserts key information into a growth model. The improved methodology does not piece the analysis together, but gives a direct MTBF mission profile estimate of the system's reliability that is directly compared to the MTBF requirement. The methodology will reflect any reliability growth improvement during the test, and will also give management a higher projected MTBF for the system mission profile reliability after delayed corrected actions are incorporated at the end of the test. In addition, the methodology also gives an estimate of the system's growth potential, and provides management metrics to evaluate whether changes in the program need to be made. A key advantage is that the methodology is well-defined and all organizations will arrive at the same reliability assessment with the same data.

==Testing Methodology==
The methodology described here will use the [[Crow Extended|Crow extended model]] for data analysis. In order to have valid Crow extended model assessments, it is required that the operational mission profile be conducted in a structured manner. Therefore, this testing methodology involves convergence and stopping points during the testing. A stopping point is when the testing is stopped for the expressed purpose of incorporating the type BD delayed corrective actions. There may be more than one stopping point during a particular testing phase. For simplicity, the methodology with only one stopping point will be described; however, the methodology can be extended to the case of more than one stopping point. A convergence point is a time during the test when all the operational mission profile tasks meet their expected averages or fall within an acceptable range. At least three convergence points are required for a well-balanced test. The end of the test, time <math>T\,\!</math>, must be a convergence point. The test times between the convergence points do not have to be the same.
 

The objective of having the convergence points is to be able to apply the Crow extended model directly in such a way that the projection and other key reliability growth parameters can be estimated in a valid fashion. To do this, the grouped data methodology is applied. Note that the methodology can also be used with the Crow-AMSAA (NHPP) model for a simpler analysis without the ability to estimate projected and growth potential reliability. See the [[Crow-AMSAA (NHPP)#Grouped_Data|Grouped Data for the Crow-AMSAA (NHPP) model]] or for the [[Crow_Extended#Grouped_Data|Crow extended model]].

==Example - Mission Profile Testing==
Consider the test-fix-find-test data set that was introduced in the [[Crow_Extended#Example_-_Test-Fix-Find-Test_Data|Crow Extended model chapter]] and is shown again in the table below. The total test time for this test is 400 hours. Note that for this example we assume one stopping point at the end of the test for the incorporation of the delayed fixes. Also, suppose that the data set represents a military system with:

* Task 1 = firing a gun.
* Task 2 = moving under environment E1.
* Task 3 = moving under environment E2.

For every hour of operation, the operational profile states that the system operates in the E1 environment for 70% of the time and in the E2 environment for 30% of the time. In addition, for each hour of operation, the gun must be fired 10 times.

{{Text-Fix-Find-Test Data}}

In general, it is difficult to manage an operational test so that these operational profiles are continuously met throughout the test. However, the operational mission profile methodology requires that these conditions be met on average at the convergence points. In practice, this almost always can be done with proper program and test management. The convergence points are set for the testing, often at interim assessment points. The process for controlling the convergence at these points involves monitoring a graph for each of the tasks.

The following table shows the expected and actual results for each of the operational mission profiles.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"

|colspan="7" style="text-align:center"|'''Expected and Actual Results for Profiles 1, 2, 3'''
|-
| ||colspan="2" style="text-align: center;" | Profile 1(gun firings)|| colspan="2" style="text-align: center;" | Profile 2(E1)|| colspan="2" style="text-align: center;" | Profile 3(E2)
|-
|Time||Expected||Actual||Expected||Actual||Expected||Actual
|-
|5|| 50|| 0|| 3.5|| 5|| 1.5|| 0
|-
|10|| 100|| 0|| 7|| 10|| 3|| 0
|-
|15|| 150|| 0|| 10.5|| 15|| 4.5|| 0
|-
|20|| 200|| 0|| 14|| 20|| 6|| 0
|-
|25|| 250|| 100|| 17.5|| 25|| 7.5|| 0
|-
|30|| 300|| 150|| 21|| 30|| 9|| 0
|-
|35|| 350|| 400|| 24.5|| 30|| 10.5|| 5
|-
|40|| 400|| 600|| 28|| 30|| 12|| 10
|-
|45|| 450|| 600|| 31.5|| 30|| 13.5|| 15
|-
|50|| 500|| 600|| 35|| 30|| 15|| 20
|-
|55|| 550|| 800|| 38.5|| 35|| 16.5|| 20
|-
|60|| 600|| 800|| 42|| 40|| 18|| 20
|-
|65|| 650|| 800|| 45.5|| 45|| 19.5|| 20
|-
|70|| 700|| 800|| 49|| 50|| 21|| 20
|-
|75|| 750|| 800|| 52.5|| 55|| 22.5|| 20
|-
|80|| 800|| 900|| 56|| 55|| 24|| 25
|-
|85|| 850|| 950|| 59.5|| 55|| 25.5|| 30
|-
|90|| 900|| 1000|| 63|| 60|| 27|| 30
|-
|95|| 950|| 1000|| 66.5|| 65|| 28.5|| 30
|-
|100|| 1000|| 1000|| 70|| 70|| 30|| 30
|-
|105|| 1050|| 1000|| 73.5|| 70|| 31.5|| 35
|-
|...||...||...||...||...||...||
|-
|...||...||...||...||...||...||
|-
|355|| 3550|| 3440|| 248.5|| 259|| 106.5|| 96
|-
|360|| 3600|| 3690|| 252|| 264|| 108|| 96
|-
|365|| 3650|| 3690|| 255.5|| 269|| 109.5|| 96
|-
|370|| 3700|| 3850|| 259|| 274|| 111|| 96
|-
|375|| 3750|| 3850|| 262.5|| 279|| 112.5|| 96
|-
|380|| 3800|| 3850|| 266|| 280|| 114|| 100
|-
|385|| 3850|| 3850|| 269.5|| 280|| 115.5|| 105
|-
|390|| 3900|| 3850|| 273|| 280|| 117|| 110
|-
|395|| 3950|| 4000|| 276.5|| 280|| 118.5|| 115
|-
|400|| 4000|| 4000|| 280|| 280|| 120|| 120
|}

The next figure shows a portion of the expected and actual results for mission profile 1, as entered in the RGA software.

[[Image:rga12.1.png|center|450px]]

A graph exists for each of the three tasks in this example. Each graph has a line with the expected average as a function of hours, and the corresponding actual value. When the actual value for a task meets the expected value then it is a convergence for that task. A convergence point occurs when all of the tasks converge at the same time. At least three convergence points are required, one of which is the stopping point <math>T\,\!</math>. In our example, the total test time is 400 hours. The convergence points were chosen to be at 100, 250, 320 and 400 hours. The next figure shows the data sheet that contains the convergence points in the RGA software.

[[Image:rga12.2.png|center|450px]]

The testing profiles are managed so that at these times the actual operational test profile equals the expected values for the three tasks or falls within an acceptable range. The next graph shows the expected and actual gun firings.

[[Image:rga12.3.png|center|450px]]

While the next two graphs show the expected and actual time in environments E1 and E2, respectively.

[[Image:rga12.4.png|center|450px]]

[[Image:rga12.5.png|center|450px]]

The objective of having the convergence points is to be able to apply the Crow extended model directly in such a way that the projection and other key reliability growth parameters can be estimated in a valid fashion. To do this, grouped data is applied using the Crow extended model. For reliability growth assessments using grouped data, only the information between time points in the testing is used. In our application, these time points are the convergence points 100, 250, 320, and 400. The next figure shows all three mission profiles plotted in the same graph, together with the convergence points.

[[Image:rga12.6.png|center|450px]]

The following table gives the grouped data input corresponding to the original data set.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="9" style="text-align:center"|'''Grouped Data at Convergence Points 100, 250, 320 and 400 Hours'''
|-
!Number at Event
!Time to Event
!Classification
!Mode
!
!Number at Event
!Time to Event
!Classification
!Mode
|-
|3|| 100|| BC|| 17|| || 1|| 250|| BC|| 26
|-
|1|| 100|| BD|| 1|| || 1|| 250|| BD|| 11
|-
|1|| 100|| BC|| 18|| || 1|| 250|| BD|| 12
|-
|1|| 100|| BD|| 2|| || 3|| 320|| A||
|-
|1|| 100|| BD|| 3|| || 1|| 320|| BD|| 1
|-
|1|| 100|| BD|| 4|| || 1|| 320|| BD|| 8
|-
|1|| 100|| BC|| 19|| || 1|| 320|| BD|| 6
|-
|2|| 100|| BD|| 5|| || 1|| 320|| BC|| 27
|-
|1|| 100|| A|| || || 1|| 320|| BD|| 13
|-
|1|| 100|| BC|| 20|| || 1|| 320|| BD|| 9
|-
|1|| 100|| BD|| 6|| || 1|| 320|| BD|| 4
|-
|1|| 250|| BD|| 7|| || 3|| 400|| A||
|-
|3|| 250|| A|| || || 1|| 400|| BD|| 12
|-
|1|| 250|| BD|| 8|| || 2|| 400|| BD|| 10
|-
|1|| 250|| BC|| 21|| || 1|| 400|| BD|| 5
|-
|1|| 250|| BD|| 2|| || 1|| 400|| BD|| 3
|-
|1|| 250|| BC|| 22|| || 1|| 400|| BC|| 28
|-
|2|| 250|| BD|| 9|| || 1|| 400|| BD|| 2
|-
|2|| 250|| BD|| 10|| || 1|| 400|| BD|| 8
|-
|1|| 250|| BC|| 23|| || 1|| 400|| BD|| 14
|-
|1|| 250|| BC|| 24|| || 1|| 400|| BD|| 15
|-
|1|| 250|| BC|| 25|| || 1|| 400|| BD|| 16
|}

The parameters of the Crow extended model for grouped data are then estimated, as explained in the Grouped Data section of the [[Crow_Extended#Grouped_Data|Crow Extended]] chapter. The following table shows the effectiveness factors (EFs) for the BD modes.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Effectiveness Factors for delayed fixes'''
|-
!Mode
!Effectiveness Factor
|-
|1|| 0.67
|-
|2|| 0.72
|-
|3|| 0.77
|-
|4|| 0.77
|-
|5|| 0.87
|-
|6|| 0.92
|-
|7|| 0.50
|-
|8|| 0.85
|-
|9|| 0.89
|-
|10|| 0.74
|-
|11|| 0.70
|-
|12|| 0.63
|-
|13|| 0.64
|-
|14|| 0.72
|-
|15|| 0.69
|-
|16|| 0.46
|}

Using the failure times data sheet shown next, we can analyze this data set based on a specified mission profile. This will group the failure times data into groups based on the convergence points that have already been specified when constructing the mission profile.

[[Image:rga12.7.png|center|600px]]

A new data sheet with the grouped data is created, as shown in the figure below and the calculated results based on the grouped data are as follows:

[[Image:rga12.9.png|center|600px]]

The following plot shows the instantaneous, demonstrated, projected and growth potential MTBF for the grouped data, based the mission profile grouping with intervals at the specified convergence points of the mission profile.

[[Image:rga12.10.png|center|450px]]

{{Examples Box|RGA Examples|More mission profile examples are available! See also:
{{Examples Link External|http://www.reliasoft.com/rga/examples/rgex7/index.htm|Mission Profile Testing}}<nowiki/>
}}

Operational Mission Profile Testing

2014-06-12T16:20:30Z

Chris Kahn: /* Example - Mission Profile Testing */

{{template:RGA BOOK|5|Operational Mission Profile Testing}}
It is common practice for systems to be subjected to operational testing during a development program. The objective of this testing is to evaluate the performance of the system, including reliability, under conditions that represent actual use. Because of budget, resources, schedule and other considerations, these operational tests rarely match exactly the actual use conditions. Usually, stated mission profile conditions are used for operational testing. These mission profile conditions are typically general statements that guide testing on an average basis. For example, a copier might be required to print 3,000 pages by time T=10 days and 5,000 pages by time T=15 days. In addition the copier is required to scan 200 documents by time T=10 days, 250 documents by time T=15 days, etc.

Because of practical constraints, these full mission profile conditions are typically not repeated one after the other during testing. Instead, the elements that make up the mission profile conditions are tested under varying schedules with the intent that, on average, the mission profile conditions are met. In practice, reliability corrective actions are generally incorporated into the system as a result of this type of testing.

Because of a lack of structure for managing the elements that make up the mission profile, it is difficult to have an agreed upon methodology for estimating the system's reliability. Many systems fail operational testing because key assessments such as growth potential and projections cannot be made in a straightforward manner so that management can take appropriate action. The RGA software addresses this issue by incorporating a systematic mission profile methodology for operational reliability testing and reliability growth assessments.

==Introduction==
Operational testing is an attempt to subject the system to conditions close to the actual environment that is expected under customer use. Often this is an extension of reliability growth testing where operation induced failure modes and corrective actions are of prime interest. Sometimes the stated intent is for a demonstration test where corrective actions are not the prime objective. However, it is not unusual for a system to fail the demonstration test, and the management issue is what to do next. In both cases, important and valid key parameters are needed to properly assess this situation and make cost-effective and timely decisions. This is often difficult in practice.

For example, a system may be required to:
* Conduct a specific task a fixed number times for each hour of operation (task 1).
* Move a fixed number of miles under a specific operating condition for each hour of operation (task 2).
* Move a fixed number of miles under another operating condition for each hour of operation (task 3).

During operational testing, these guidelines are met individually as averages. For example, the actual as-tested profile for task 1 may not be uniform relative to the stated mission guidelines during the testing. What is often the case is that some of the tasks (for example task 1) could be operated below the stated guidelines. This can mask a major reliability problem. In other cases during testing, tasks 1, 2 and 3 might never meet their stated averages, except perhaps at the end of the test. This becomes an issue because an important aspect of effective reliability risk management is to not wait until the end of the test to have an assessment of the reliability performance.

Because the elements of the mission profile during the testing will rarely, if ever, balance continuously to the stated averages, a common analysis method is to piece the reliability assessments together by evaluating each element of the profile separately. This is not a well-defined methodology and does not account for improvement during the testing. It is therefore not unusual for two separate organizations (e.g., the customer and the developer) to analyze the same data and obtain different MTBF numbers. In addition, this method does not address the delayed corrective actions that are to be incorporated at the end of the test nor does it estimate growth potential or interaction effects. Therefore, to reduce this risk there is a need for a rigorous methodology for reliability during operational testing that does not rely on piecewise analysis and avoids the issues noted above.

The RGA software incorporates a new methodology to manage system reliability during operational mission profile testing. This methodology draws information from particular plots of the operational test data and inserts key information into a growth model. The improved methodology does not piece the analysis together, but gives a direct MTBF mission profile estimate of the system's reliability that is directly compared to the MTBF requirement. The methodology will reflect any reliability growth improvement during the test, and will also give management a higher projected MTBF for the system mission profile reliability after delayed corrected actions are incorporated at the end of the test. In addition, the methodology also gives an estimate of the system's growth potential, and provides management metrics to evaluate whether changes in the program need to be made. A key advantage is that the methodology is well-defined and all organizations will arrive at the same reliability assessment with the same data.

==Testing Methodology==
The methodology described here will use the [[Crow Extended|Crow extended model]] for data analysis. In order to have valid Crow extended model assessments, it is required that the operational mission profile be conducted in a structured manner. Therefore, this testing methodology involves convergence and stopping points during the testing. A stopping point is when the testing is stopped for the expressed purpose of incorporating the type BD delayed corrective actions. There may be more than one stopping point during a particular testing phase. For simplicity, the methodology with only one stopping point will be described; however, the methodology can be extended to the case of more than one stopping point. A convergence point is a time during the test when all the operational mission profile tasks meet their expected averages or fall within an acceptable range. At least three convergence points are required for a well-balanced test. The end of the test, time <math>T\,\!</math>, must be a convergence point. The test times between the convergence points do not have to be the same.
 

The objective of having the convergence points is to be able to apply the Crow extended model directly in such a way that the projection and other key reliability growth parameters can be estimated in a valid fashion. To do this, the grouped data methodology is applied. Note that the methodology can also be used with the Crow-AMSAA (NHPP) model for a simpler analysis without the ability to estimate projected and growth potential reliability. See the [[Crow-AMSAA (NHPP)#Grouped_Data|Grouped Data for the Crow-AMSAA (NHPP) model]] or for the [[Crow_Extended#Grouped_Data|Crow extended model]].

==Example - Mission Profile Testing==
Consider the test-fix-find-test data set that was introduced in the [[Crow_Extended#Example_-_Test-Fix-Find-Test_Data|Crow Extended model chapter]] and is shown again in the table below. The total test time for this test is 400 hours. Note that for this example we assume one stopping point at the end of the test for the incorporation of the delayed fixes. Also, suppose that the data set represents a military system with:

* Task 1 = firing a gun.
* Task 2 = moving under environment E1.
* Task 3 = moving under environment E2.

For every hour of operation, the operational profile states that the system operates in the E1 environment for 70% of the time and in the E2 environment for 30% of the time. In addition, for each hour of operation, the gun must be fired 10 times.

{{Text-Fix-Find-Test Data}}

In general, it is difficult to manage an operational test so that these operational profiles are continuously met throughout the test. However, the operational mission profile methodology requires that these conditions be met on average at the convergence points. In practice, this almost always can be done with proper program and test management. The convergence points are set for the testing, often at interim assessment points. The process for controlling the convergence at these points involves monitoring a graph for each of the tasks.

The following table shows the expected and actual results for each of the operational mission profiles.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"

|colspan="7" style="text-align:center"|'''Expected and Actual Results for Profiles 1, 2, 3'''
|-
| ||colspan="2" style="text-align: center;" | Profile 1(gun firings)|| colspan="2" style="text-align: center;" | Profile 2(E1)|| colspan="2" style="text-align: center;" | Profile 3(E2)
|-
|Time||Expected||Actual||Expected||Actual||Expected||Actual
|-
|5|| 50|| 0|| 3.5|| 5|| 1.5|| 0
|-
|10|| 100|| 0|| 7|| 10|| 3|| 0
|-
|15|| 150|| 0|| 10.5|| 15|| 4.5|| 0
|-
|20|| 200|| 0|| 14|| 20|| 6|| 0
|-
|25|| 250|| 100|| 17.5|| 25|| 7.5|| 0
|-
|30|| 300|| 150|| 21|| 30|| 9|| 0
|-
|35|| 350|| 400|| 24.5|| 30|| 10.5|| 5
|-
|40|| 400|| 600|| 28|| 30|| 12|| 10
|-
|45|| 450|| 600|| 31.5|| 30|| 13.5|| 15
|-
|50|| 500|| 600|| 35|| 30|| 15|| 20
|-
|55|| 550|| 800|| 38.5|| 35|| 16.5|| 20
|-
|60|| 600|| 800|| 42|| 40|| 18|| 20
|-
|65|| 650|| 800|| 45.5|| 45|| 19.5|| 20
|-
|70|| 700|| 800|| 49|| 50|| 21|| 20
|-
|75|| 750|| 800|| 52.5|| 55|| 22.5|| 20
|-
|80|| 800|| 900|| 56|| 55|| 24|| 25
|-
|85|| 850|| 950|| 59.5|| 55|| 25.5|| 30
|-
|90|| 900|| 1000|| 63|| 60|| 27|| 30
|-
|95|| 950|| 1000|| 66.5|| 65|| 28.5|| 30
|-
|100|| 1000|| 1000|| 70|| 70|| 30|| 30
|-
|105|| 1050|| 1000|| 73.5|| 70|| 31.5|| 35
|-
|...||...||...||...||...||...||
|-
|...||...||...||...||...||...||
|-
|355|| 3550|| 3440|| 248.5|| 259|| 106.5|| 96
|-
|360|| 3600|| 3690|| 252|| 264|| 108|| 96
|-
|365|| 3650|| 3690|| 255.5|| 269|| 109.5|| 96
|-
|370|| 3700|| 3850|| 259|| 274|| 111|| 96
|-
|375|| 3750|| 3850|| 262.5|| 279|| 112.5|| 96
|-
|380|| 3800|| 3850|| 266|| 280|| 114|| 100
|-
|385|| 3850|| 3850|| 269.5|| 280|| 115.5|| 105
|-
|390|| 3900|| 3850|| 273|| 280|| 117|| 110
|-
|395|| 3950|| 4000|| 276.5|| 280|| 118.5|| 115
|-
|400|| 4000|| 4000|| 280|| 280|| 120|| 120
|}

The next figure shows a portion of the expected and actual results for mission profile 1, as entered in the RGA software.

[[Image:rga12.1.png|center|450px]]

A graph exists for each of the three tasks in this example. Each graph has a line with the expected average as a function of hours, and the corresponding actual value. When the actual value for a task meets the expected value then it is a convergence for that task. A convergence point occurs when all of the tasks converge at the same time. At least three convergence points are required, one of which is the stopping point <math>T\,\!</math>. In our example, the total test time is 400 hours. The convergence points were chosen to be at 100, 250, 320 and 400 hours. The next figure shows the data sheet that contains the convergence points in the RGA software.

[[Image:rga12.2.png|center|450px]]

The testing profiles are managed so that at these times the actual operational test profile equals the expected values for the three tasks or falls within an acceptable range. The next graph shows the expected and actual gun firings.

[[Image:rga12.3.png|center|450px]]

While the next two graphs show the expected and actual time in environments E1 and E2, respectively.

[[Image:rga12.4.png|center|450px]]

[[Image:rga12.5.png|center|450px]]

The objective of having the convergence points is to be able to apply the Crow extended model directly in such a way that the projection and other key reliability growth parameters can be estimated in a valid fashion. To do this, grouped data is applied using the Crow extended model. For reliability growth assessments using grouped data, only the information between time points in the testing is used. In our application, these time points are the convergence points 100, 250, 320, and 400. The next figure shows all three mission profiles plotted in the same graph, together with the convergence points.

[[Image:rga12.6.png|center|450px]]

The following table gives the grouped data input corresponding to the original data set.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="9" style="text-align:center"|'''Grouped data at convergence points 100, 250, 320 and 400 hours'''
|-
!Number at Event
!Time to Event
!Classification
!Mode
!
!Number at Event
!Time to Event
!Classification
!Mode
|-
|3|| 100|| BC|| 17|| || 1|| 250|| BC|| 26
|-
|1|| 100|| BD|| 1|| || 1|| 250|| BD|| 11
|-
|1|| 100|| BC|| 18|| || 1|| 250|| BD|| 12
|-
|1|| 100|| BD|| 2|| || 3|| 320|| A||
|-
|1|| 100|| BD|| 3|| || 1|| 320|| BD|| 1
|-
|1|| 100|| BD|| 4|| || 1|| 320|| BD|| 8
|-
|1|| 100|| BC|| 19|| || 1|| 320|| BD|| 6
|-
|2|| 100|| BD|| 5|| || 1|| 320|| BC|| 27
|-
|1|| 100|| A|| || || 1|| 320|| BD|| 13
|-
|1|| 100|| BC|| 20|| || 1|| 320|| BD|| 9
|-
|1|| 100|| BD|| 6|| || 1|| 320|| BD|| 4
|-
|1|| 250|| BD|| 7|| || 3|| 400|| A||
|-
|3|| 250|| A|| || || 1|| 400|| BD|| 12
|-
|1|| 250|| BD|| 8|| || 2|| 400|| BD|| 10
|-
|1|| 250|| BC|| 21|| || 1|| 400|| BD|| 5
|-
|1|| 250|| BD|| 2|| || 1|| 400|| BD|| 3
|-
|1|| 250|| BC|| 22|| || 1|| 400|| BC|| 28
|-
|2|| 250|| BD|| 9|| || 1|| 400|| BD|| 2
|-
|2|| 250|| BD|| 10|| || 1|| 400|| BD|| 8
|-
|1|| 250|| BC|| 23|| || 1|| 400|| BD|| 14
|-
|1|| 250|| BC|| 24|| || 1|| 400|| BD|| 15
|-
|1|| 250|| BC|| 25|| || 1|| 400|| BD|| 16
|}

The parameters of the Crow extended model for grouped data are then estimated, as explained in the Grouped Data section of the [[Crow_Extended#Grouped_Data|Crow Extended]] chapter. The following table shows the effectiveness factors (EFs) for the BD modes.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Effectiveness Factors for delayed fixes'''
|-
!Mode
!Effectiveness Factor
|-
|1|| 0.67
|-
|2|| 0.72
|-
|3|| 0.77
|-
|4|| 0.77
|-
|5|| 0.87
|-
|6|| 0.92
|-
|7|| 0.50
|-
|8|| 0.85
|-
|9|| 0.89
|-
|10|| 0.74
|-
|11|| 0.70
|-
|12|| 0.63
|-
|13|| 0.64
|-
|14|| 0.72
|-
|15|| 0.69
|-
|16|| 0.46
|}

Using the failure times data sheet shown next, we can analyze this data set based on a specified mission profile. This will group the failure times data into groups based on the convergence points that have already been specified when constructing the mission profile.

[[Image:rga12.7.png|center|600px]]

A new data sheet with the grouped data is created, as shown in the figure below and the calculated results based on the grouped data are as follows:

[[Image:rga12.9.png|center|600px]]

The following plot shows the instantaneous, demonstrated, projected and growth potential MTBF for the grouped data, based the mission profile grouping with intervals at the specified convergence points of the mission profile.

[[Image:rga12.10.png|center|450px]]

{{Examples Box|RGA Examples|More mission profile examples are available! See also:
{{Examples Link External|http://www.reliasoft.com/rga/examples/rgex7/index.htm|Mission Profile Testing}}<nowiki/>
}}

Fleet Data Analysis

2014-06-12T16:19:35Z

Chris Kahn: /* Applying the Crow Extended Model to Fleet Data */

{{template:RGA BOOK|6.3|Fleet Data Analysis}}
Fleet analysis is similar to the [[Repairable Systems Analysis|repairable systems analysis]] described in the previous chapter. The main difference is that a fleet of systems is considered and the models are applied to the fleet failures rather than to the system failures. In other words, repairable system analysis models the number of system failures versus system time, whereas fleet analysis models the number of fleet failures versus fleet time.
 

The main motivation for fleet analysis is to enable the application of the Crow Extended model for fielded data. In many cases, reliability improvements might be necessary on systems that are already in the field. These types of reliability improvements are essentially delayed fixes (BD modes) as described in the [[Crow Extended]] chapter.
 

==Introduction==
Recall from the previous chapter that in order to make projections using the [[Crow Extended]] model, the <math>\beta \,\!</math> of the combined A and BD modes should be equal to 1. Since the failure intensity in a fielded system might be changing over time (e.g., increasing if the system wears out), this assumption might be violated. In such a scenario, the Crow Extended model cannot be used. However, if a fleet of systems is considered and the number of fleet failures versus fleet time is modeled, the failures might become random. This is because there is a mixture of systems within a fleet, new and old, and when the failures of this mixture of systems are viewed from a cumulative fleet time point of view, they may be random. The next two figures illustrate this concept. The first picture shows the number of failures over system age. It can be clearly seen that as the systems age, the intensity of the failures increases (wearout). The superposition system line, which brings the failures from the different systems under a single timeline, also illustrates this observation. On the other hand, if you take the same four systems and combine their failures from a fleet perspective, and consider fleet failures over cumulative fleet hours, then the failures seem to be random. The second picture illustrates this concept in the System Operation plot when you consider the Cum. Time Line. In this case, the <math>\beta \,\!</math> of the fleet will be equal to 1 and the Crow Extended model can be used for quantifying the effects of future reliability improvements on the fleet.

[[Image:rga13.5.png|thumb|center|400px|Repairable System Operation plot.]]

[[Image:rga13.6.png|thumb|center|400px|Fleet System Operation plot.]]

==Methodology==
The figures above illustrate that the difference between repairable system data analysis and fleet analysis is the way that the data set is treated. In fleet analysis, the time-to-failure data from each system is stacked to a cumulative timeline. For example, consider the two systems in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"|'''System Data'''
|-
!System
!Failure Times (hr)
!End Time (hr)
|-
|1|| 3, 7|| 10
|-
|2|| 4, 9, 13|| 15
|}

===Convert to Accumulated Timeline===
The data set is first converted to an accumulated timeline, as follows:

*System 1 is considered first. The accumulated timeline is therefore 3 and 7 hours.
*System 1's end time is 10 hours. System 2's first failure is at 4 hours. This failure time is added to System 1's end time to give an accumulated failure time of 14 hours.
*The second failure for System 2 occurred 5 hours after the first failure. This time interval is added to the accumulated timeline to give 19 hours.
*The third failure for System 2 occurred 4 hours after the second failure. The accumulated failure time is 19 + 4 = 23 hours.
*System 2's end time is 15 hours, or 2 hours after the last failure. The total accumulated operating time for the fleet is 25 hours (23 + 2 = 25).

In general, the accumulated operating time <math>{{Y}_{j}}\,\!</math> is calculated by:

:<math>{{Y}_{j}}={{X}_{i,q}}+\underset{q=1}{\overset{K-1}{\mathop \sum }}\,{{T}_{q}},\text{ }m=1,2,...,N\,\!</math>

where:

*<math>{{X}_{i,q}}\,\!</math> is the <math>{{i}^{th}}\,\!</math> failure of the <math>{{q}^{th}}\,\!</math> system
*<math>{{T}_{q}}\,\!</math> is the end time of the <math>{{q}^{th}}\,\!</math> system
*<math>K\,\!</math> is the total number of systems
*<math>N\,\!</math> is the total number of failures from all systems ( <math>N=\underset{j=1}{\overset{K}{\mathop{\sum }}}\,{{N}_{q}}\,\!</math> )

As this example demonstrates, the accumulated timeline is determined based on the order of the systems. So if you consider the data in the table by taking System 2 first, the accumulated timeline would be: 4, 9, 13, 18, 22, with an end time of 25. Therefore, the order in which the systems are considered is somewhat important. However, in the next step of the analysis, the data from the accumulated timeline will be grouped into time intervals, effectively eliminating the importance of the order of the systems. Keep in mind that this will NOT always be true. This is true only when the order of the systems was random to begin with. If there is some logic/pattern in the order of the systems, then it will remain even if the cumulative timeline is converted to grouped data. For example, consider a system that wears out with age. This means that more failures will be observed as this system ages and these failures will occur more frequently. Within a fleet of such systems, there will be new and old systems in operation. If the data set collected is considered from the newest to the oldest system, then even if the data points are grouped, the pattern of fewer failures at the beginning and more failures at later time intervals will still be present. If the objective of the analysis is to determine the difference between newer and older systems, then that order for the data will be acceptable. However, if the objective of the analysis is to determine the reliability of the fleet, then the systems should be randomly ordered.

===Analyze the Grouped Data===
Once the accumulated timeline has been generated, it is then converted into grouped data. To accomplish this, a group interval is required. The group interval length should be chosen so that it is representative of the data. Also note that the intervals do not have to be of equal length. Once the data points have been grouped, the parameters can be obtained using maximum likelihood estimation as described in the [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP) chapter]]. The data from the table above can be grouped into 5 hour intervals. This interval length is sufficiently large to insure that there are failures within each interval. The grouped data set is given in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Grouped Data'''
|-
!Failures in Interval
!Interval End Time
|-
|1|| 5
|-
|1|| 10
|-
|1|| 15
|-
|1|| 20
|-
|1|| 25
|}

The Crow-AMSAA model for grouped failure times is used for the data, and the parameters of the model are solved by satisfying the following maximum likelihood equations (See [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP)]]):

:<math>\widehat{\lambda }=\frac{n}{T_{k}^{\widehat{\beta }}}\,\!</math>

:<math>\underset{i=1}{\overset{k}{\mathop \sum }}\,{{n}_{i}}\left[ \frac{T_{i}^{\widehat{\beta }}\ln {{T}_{i-1}}-T_{i-1}^{\widehat{\beta }}\ln {{T}_{i-1}}}{T_{i}^{\widehat{\beta }}-T_{i-1}^{\widehat{\beta }}}-\ln {{T}_{k}} \right]=0 </math>

==Fleet Analysis Example==
{{:Fleet_Analysis_Example}}

==Applying the Crow Extended Model to Fleet Data==
As it was mentioned previously, the main motivation of the fleet analysis is to apply the Crow Extended model for in-service reliability improvements. The methodology to be used is identical to the application of the [[Crow_Extended#Grouped_Data|Crow Extended model for Grouped Data]] described in a previous chapter. Consider the fleet data from the example above. In order to apply the Crow Extended model, put <math>N=37\,\!</math> failure times on a cumulative time scale over <math>(0,T)\,\!</math>, where <math>T=52110\,\!</math>. In the example, each <math>{{T}_{i}}\,\!</math> corresponds to a failure time <math>{{X}_{ij}}\,\!</math>. This is often not the situation. However, in all cases the accumulated operating time <math>{{Y}_{q}}\,\!</math> at a failure time <math>{{X}_{ir}}\,\!</math> is:

:<math>\begin{align}
{{Y}_{q}}= & {{X}_{i,r}}+\underset{j=1}{\overset{r-1}{\mathop \sum }}\,{{T}_{j}},\ \ \ q=1,2,\ldots ,N \\
N= & \underset{j=1}{\overset{K}{\mathop \sum }}\,{{N}_{j}}
\end{align}\,\!</math>

And <math>q\,\!</math> indexes the successive order of the failures. Thus, in this example <math>N=37,\,{{Y}_{1}}=1396,\,{{Y}_{2}}=5893,\,{{Y}_{3}}=6418,\ldots ,{{Y}_{37}}=52110\,\!</math>. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="7" style="text-align:center"|'''Test-Find-Test Fleet Data'''
|-
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
!
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
|-
|1|| 1396|| BD1|| || 20|| 26361|| BD1
|-
|2|| 5893|| BD2|| || 21|| 26392|| A
|-
|3|| 6418|| A|| || 22|| 26845|| BD8
|-
|4|| 7650|| BD3|| || 23|| 30477|| BD1
|-
|5|| 7877|| BD4|| || 24|| 31500|| A
|-
|6|| 8012|| BD2|| || 25|| 31661|| BD3
|-
|7|| 8031|| BD2|| || 26|| 31697|| BD2
|-
|8|| 8843|| BD1|| || 27|| 36428|| BD1
|-
|9|| 10867|| BD1|| || 28|| 40223|| BD1
|-
|10|| 11183|| BD5|| || 29|| 40803|| BD9
|-
|11|| 11810|| A|| || 30|| 42656|| BD1
|-
|12|| 11870|| BD1|| || 31|| 42724|| BD10
|-
|13|| 16139|| BD2|| || 32|| 44554|| BD1
|-
|14|| 16104|| BD6|| || 33|| 45795|| BD11
|-
|15|| 18178|| BD7|| || 34|| 46666|| BD12
|-
|16|| 18677|| BD2|| || 35|| 48368|| BD1
|-
|17|| 20751|| BD4|| || 36|| 51924|| BD13
|-
|18|| 20772|| BD2|| || 37|| 52110|| BD2
|-
|19|| 25815|| BD1|| || ||
|}

Each system failure time in the table above corresponds to a problem and a cause (failure mode). The management strategy can be to not fix the failure mode (A mode) or to fix the failure mode with a delayed corrective action (BD mode). There are <math>{{N}_{A}}=4\,\!</math> failures due to A failure modes. There are <math>{{N}_{BD}}=33\,\!</math> total failures due to <math>M=13\,\!</math> distinct BD failure modes. Some of the distinct BD modes had repeats of the same problem. For example, mode BD1 had 12 occurrences of the same problem. Therefore, in this example, there are 13 distinct corrective actions corresponding to 13 distinct BD failure modes.

The objective of the Crow Extended model is to estimate the impact of the 13 distinct corrective actions.The analyst will choose an average effectiveness factor (EF) based on the proposed corrective actions and historical experience. Historical industry and government data supports a typical average effectiveness factor <math>\overline{d}=.70\,\!</math> for many systems. In this example, an average EF of <math>\bar{d}=0.4\,\!</math> was assumed in order to be conservative regarding the impact of the proposed corrective actions. Since there are no BC failure modes (corrective actions applied during the test), the projected failure intensity is:

:<math>\widehat{r}(T)=\left( \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \right)+\overline{d}h(T)\,\!</math>

The first term is estimated by:

:<math>{{\widehat{\lambda }}_{A}}=\frac{{{N}_{A}}}{T}=0.000077\,\!</math>

The second term is:

:<math>\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}=0.00038\,\!</math>

This estimates the growth potential failure intensity:

:<math>\begin{align}
{{\widehat{\gamma }}_{GP}}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \\
= & 0.00046
\end{align}\,\!</math>

To estimate the last term <math>\overline{d}h(T)\,\!</math> of the Crow Extended model, partition the data in the table into intervals. This partition consists of <math>D\,\!</math> successive intervals. The length of the <math>{{q}^{th}}\,\!</math> interval is <math>{{L}_{q}},\,\!</math> <math>\,q=1,2,\ldots ,D\,\!</math>. It is not required that the intervals be of the same length, but there should be several (e.g., at least 5) cycles per interval on average. Also, let <math>{{S}_{1}}={{L}_{1}},\,\!</math> <math>{{S}_{2}}={{L}_{1}}+{{L}_{2}},\ldots ,\,\!</math> etc. be the accumulated time through the <math>{{q}^{th}}\,\!</math> interval. For the <math>{{q}^{th}}\,\!</math> interval, note the number of distinct BD modes, <math>M{{I}_{q}}\,\!</math>, appearing for the first time, <math>q=1,2,\ldots ,D\,\!</math>. See the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped Data for Distinct BD Modes'''
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| <math>\text{MI}_{1}\,\!</math> || <math>\text{L}_{1}\,\!</math> || <math>\text{S}_{1}\,\!</math>
|-
|2|| <math>\text{MI}_{2}\,\!</math>|| <math>\text{L}_{2}\,\!</math>|| <math>\text{S}_{2}\,\!</math>
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|D|| <math>\text{MI}_{D}\,\!</math> || <math>\text{L}_{D}\,\!</math>|| <math>\text{S}_{D}\,\!</math>
|}

The term <math>\widehat{h}(T)\,\!</math> is calculated as <math>\widehat{h}(T)=\widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}}\,\!</math> and the values <math>\widehat{\lambda }\,\!</math> and <math>\widehat{\beta }\,\!</math> satisfy the maximum likelihood equations for grouped data (given in [[Fleet_Data_Analysis#Analyze_the_Grouped_Data|the Methodology section]]). This is the grouped data version of the Crow-AMSAA model applied only to the first occurrence of distinct BD modes.

For the data in the first table, the first 4 intervals had a length of 10,000 and the last interval was 12,110. Therefore, <math>D=5\,\!</math>. This choice gives an average of about 5 overhaul cycles per interval. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped Data for Distinct BD Modes from Data in "[[Fleet_Data_Analysis#Applying_the_Crow_Extended_Model_to_Fleet_Data|Applying the Crow Extended Model to Fleet Data]]"
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| 4|| 10000|| 10000
|-
|2|| 3|| 10000|| 20000
|-
|3|| 1|| 10000|| 30000
|-
|4|| 0|| 10000|| 40000
|-
|5|| 5|| 12110|| 52110
|-
|Total|| 13||
|}

Thus:

:<math>\begin{align}
\widehat{\lambda }= & 0.00330 \\
\widehat{\beta }= & 0.76219
\end{align}\,\!</math>

This gives:

:<math>\begin{align}
\widehat{h}(T)= & \widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}} \\
= & 0.00019
\end{align}\,\!</math>

Consequently, for <math>\overline{d}=0.4\,\!</math> the last term of the Crow Extended model is given by:

:<math>\overline{d}h(T)=0.000076\,\!</math>

The projected failure intensity is:

:<math>\begin{align}
\widehat{r}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}+\overline{d}h(T) \\
= & 0.000077+0.6\times (0.00063)+0.4\times (0.00019) \\
= & 0.000533
\end{align}\,\!</math>

This estimates that the 13 proposed corrective actions will reduce the number of failures per cycle of operation hours from the current <math>\widehat{r}(0)=\tfrac{{{N}_{A}}+{{N}_{BD}}}{T}=0.00071\,\!</math> to <math>\widehat{r}(T)=0.00053.\,\!</math> The average time between failures is estimated to increase from the current 1408.38 hours to 1876.93 hours.

==Confidence Bounds==
For fleet data analysis using the Crow-AMSAA model, the confidence bounds are calculated using the same procedure described for the Crow-AMSAA (NHPP) model (See [[Crow-AMSAA Confidence Bounds]]). For fleet data analysis using the Crow Extended model, the confidence bounds are calculated using the same procedure described for the Crow Extended model (See [[Crow Extended Confidence Bounds]]).

=More Examples=
==Predicting the Number of Failures for Fleet Operation==
{{:Crow_Extended_Model_Fleet_Analysis_Example}}

Fleet Data Analysis

2014-06-12T16:17:18Z

Chris Kahn: /* Applying the Crow Extended Model to Fleet Data */

{{template:RGA BOOK|6.3|Fleet Data Analysis}}
Fleet analysis is similar to the [[Repairable Systems Analysis|repairable systems analysis]] described in the previous chapter. The main difference is that a fleet of systems is considered and the models are applied to the fleet failures rather than to the system failures. In other words, repairable system analysis models the number of system failures versus system time, whereas fleet analysis models the number of fleet failures versus fleet time.
 

The main motivation for fleet analysis is to enable the application of the Crow Extended model for fielded data. In many cases, reliability improvements might be necessary on systems that are already in the field. These types of reliability improvements are essentially delayed fixes (BD modes) as described in the [[Crow Extended]] chapter.
 

==Introduction==
Recall from the previous chapter that in order to make projections using the [[Crow Extended]] model, the <math>\beta \,\!</math> of the combined A and BD modes should be equal to 1. Since the failure intensity in a fielded system might be changing over time (e.g., increasing if the system wears out), this assumption might be violated. In such a scenario, the Crow Extended model cannot be used. However, if a fleet of systems is considered and the number of fleet failures versus fleet time is modeled, the failures might become random. This is because there is a mixture of systems within a fleet, new and old, and when the failures of this mixture of systems are viewed from a cumulative fleet time point of view, they may be random. The next two figures illustrate this concept. The first picture shows the number of failures over system age. It can be clearly seen that as the systems age, the intensity of the failures increases (wearout). The superposition system line, which brings the failures from the different systems under a single timeline, also illustrates this observation. On the other hand, if you take the same four systems and combine their failures from a fleet perspective, and consider fleet failures over cumulative fleet hours, then the failures seem to be random. The second picture illustrates this concept in the System Operation plot when you consider the Cum. Time Line. In this case, the <math>\beta \,\!</math> of the fleet will be equal to 1 and the Crow Extended model can be used for quantifying the effects of future reliability improvements on the fleet.

[[Image:rga13.5.png|thumb|center|400px|Repairable System Operation plot.]]

[[Image:rga13.6.png|thumb|center|400px|Fleet System Operation plot.]]

==Methodology==
The figures above illustrate that the difference between repairable system data analysis and fleet analysis is the way that the data set is treated. In fleet analysis, the time-to-failure data from each system is stacked to a cumulative timeline. For example, consider the two systems in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"|'''System Data'''
|-
!System
!Failure Times (hr)
!End Time (hr)
|-
|1|| 3, 7|| 10
|-
|2|| 4, 9, 13|| 15
|}

===Convert to Accumulated Timeline===
The data set is first converted to an accumulated timeline, as follows:

*System 1 is considered first. The accumulated timeline is therefore 3 and 7 hours.
*System 1's end time is 10 hours. System 2's first failure is at 4 hours. This failure time is added to System 1's end time to give an accumulated failure time of 14 hours.
*The second failure for System 2 occurred 5 hours after the first failure. This time interval is added to the accumulated timeline to give 19 hours.
*The third failure for System 2 occurred 4 hours after the second failure. The accumulated failure time is 19 + 4 = 23 hours.
*System 2's end time is 15 hours, or 2 hours after the last failure. The total accumulated operating time for the fleet is 25 hours (23 + 2 = 25).

In general, the accumulated operating time <math>{{Y}_{j}}\,\!</math> is calculated by:

:<math>{{Y}_{j}}={{X}_{i,q}}+\underset{q=1}{\overset{K-1}{\mathop \sum }}\,{{T}_{q}},\text{ }m=1,2,...,N\,\!</math>

where:

*<math>{{X}_{i,q}}\,\!</math> is the <math>{{i}^{th}}\,\!</math> failure of the <math>{{q}^{th}}\,\!</math> system
*<math>{{T}_{q}}\,\!</math> is the end time of the <math>{{q}^{th}}\,\!</math> system
*<math>K\,\!</math> is the total number of systems
*<math>N\,\!</math> is the total number of failures from all systems ( <math>N=\underset{j=1}{\overset{K}{\mathop{\sum }}}\,{{N}_{q}}\,\!</math> )

As this example demonstrates, the accumulated timeline is determined based on the order of the systems. So if you consider the data in the table by taking System 2 first, the accumulated timeline would be: 4, 9, 13, 18, 22, with an end time of 25. Therefore, the order in which the systems are considered is somewhat important. However, in the next step of the analysis, the data from the accumulated timeline will be grouped into time intervals, effectively eliminating the importance of the order of the systems. Keep in mind that this will NOT always be true. This is true only when the order of the systems was random to begin with. If there is some logic/pattern in the order of the systems, then it will remain even if the cumulative timeline is converted to grouped data. For example, consider a system that wears out with age. This means that more failures will be observed as this system ages and these failures will occur more frequently. Within a fleet of such systems, there will be new and old systems in operation. If the data set collected is considered from the newest to the oldest system, then even if the data points are grouped, the pattern of fewer failures at the beginning and more failures at later time intervals will still be present. If the objective of the analysis is to determine the difference between newer and older systems, then that order for the data will be acceptable. However, if the objective of the analysis is to determine the reliability of the fleet, then the systems should be randomly ordered.

===Analyze the Grouped Data===
Once the accumulated timeline has been generated, it is then converted into grouped data. To accomplish this, a group interval is required. The group interval length should be chosen so that it is representative of the data. Also note that the intervals do not have to be of equal length. Once the data points have been grouped, the parameters can be obtained using maximum likelihood estimation as described in the [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP) chapter]]. The data from the table above can be grouped into 5 hour intervals. This interval length is sufficiently large to insure that there are failures within each interval. The grouped data set is given in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Grouped Data'''
|-
!Failures in Interval
!Interval End Time
|-
|1|| 5
|-
|1|| 10
|-
|1|| 15
|-
|1|| 20
|-
|1|| 25
|}

The Crow-AMSAA model for grouped failure times is used for the data, and the parameters of the model are solved by satisfying the following maximum likelihood equations (See [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP)]]):

:<math>\widehat{\lambda }=\frac{n}{T_{k}^{\widehat{\beta }}}\,\!</math>

:<math>\underset{i=1}{\overset{k}{\mathop \sum }}\,{{n}_{i}}\left[ \frac{T_{i}^{\widehat{\beta }}\ln {{T}_{i-1}}-T_{i-1}^{\widehat{\beta }}\ln {{T}_{i-1}}}{T_{i}^{\widehat{\beta }}-T_{i-1}^{\widehat{\beta }}}-\ln {{T}_{k}} \right]=0 </math>

==Fleet Analysis Example==
{{:Fleet_Analysis_Example}}

==Applying the Crow Extended Model to Fleet Data==
As it was mentioned previously, the main motivation of the fleet analysis is to apply the Crow Extended model for in-service reliability improvements. The methodology to be used is identical to the application of the [[Crow_Extended#Grouped_Data|Crow Extended model for Grouped Data]] described in a previous chapter. Consider the fleet data from the example above. In order to apply the Crow Extended model, put <math>N=37\,\!</math> failure times on a cumulative time scale over <math>(0,T)\,\!</math>, where <math>T=52110\,\!</math>. In the example, each <math>{{T}_{i}}\,\!</math> corresponds to a failure time <math>{{X}_{ij}}\,\!</math>. This is often not the situation. However, in all cases the accumulated operating time <math>{{Y}_{q}}\,\!</math> at a failure time <math>{{X}_{ir}}\,\!</math> is:

:<math>\begin{align}
{{Y}_{q}}= & {{X}_{i,r}}+\underset{j=1}{\overset{r-1}{\mathop \sum }}\,{{T}_{j}},\ \ \ q=1,2,\ldots ,N \\
N= & \underset{j=1}{\overset{K}{\mathop \sum }}\,{{N}_{j}}
\end{align}\,\!</math>

And <math>q\,\!</math> indexes the successive order of the failures. Thus, in this example <math>N=37,\,{{Y}_{1}}=1396,\,{{Y}_{2}}=5893,\,{{Y}_{3}}=6418,\ldots ,{{Y}_{37}}=52110\,\!</math>. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="7" style="text-align:center"|'''Test-Find-Test Fleet Data'''
|-
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
!
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
|-
|1|| 1396|| BD1|| || 20|| 26361|| BD1
|-
|2|| 5893|| BD2|| || 21|| 26392|| A
|-
|3|| 6418|| A|| || 22|| 26845|| BD8
|-
|4|| 7650|| BD3|| || 23|| 30477|| BD1
|-
|5|| 7877|| BD4|| || 24|| 31500|| A
|-
|6|| 8012|| BD2|| || 25|| 31661|| BD3
|-
|7|| 8031|| BD2|| || 26|| 31697|| BD2
|-
|8|| 8843|| BD1|| || 27|| 36428|| BD1
|-
|9|| 10867|| BD1|| || 28|| 40223|| BD1
|-
|10|| 11183|| BD5|| || 29|| 40803|| BD9
|-
|11|| 11810|| A|| || 30|| 42656|| BD1
|-
|12|| 11870|| BD1|| || 31|| 42724|| BD10
|-
|13|| 16139|| BD2|| || 32|| 44554|| BD1
|-
|14|| 16104|| BD6|| || 33|| 45795|| BD11
|-
|15|| 18178|| BD7|| || 34|| 46666|| BD12
|-
|16|| 18677|| BD2|| || 35|| 48368|| BD1
|-
|17|| 20751|| BD4|| || 36|| 51924|| BD13
|-
|18|| 20772|| BD2|| || 37|| 52110|| BD2
|-
|19|| 25815|| BD1|| || ||
|}

Each system failure time in the table above corresponds to a problem and a cause (failure mode). The management strategy can be to not fix the failure mode (A mode) or to fix the failure mode with a delayed corrective action (BD mode). There are <math>{{N}_{A}}=4\,\!</math> failures due to A failure modes. There are <math>{{N}_{BD}}=33\,\!</math> total failures due to <math>M=13\,\!</math> distinct BD failure modes. Some of the distinct BD modes had repeats of the same problem. For example, mode BD1 had 12 occurrences of the same problem. Therefore, in this example, there are 13 distinct corrective actions corresponding to 13 distinct BD failure modes.

The objective of the Crow Extended model is to estimate the impact of the 13 distinct corrective actions.The analyst will choose an average effectiveness factor (EF) based on the proposed corrective actions and historical experience. Historical industry and government data supports a typical average effectiveness factor <math>\overline{d}=.70\,\!</math> for many systems. In this example, an average EF of <math>\bar{d}=0.4\,\!</math> was assumed in order to be conservative regarding the impact of the proposed corrective actions. Since there are no BC failure modes (corrective actions applied during the test), the projected failure intensity is:

:<math>\widehat{r}(T)=\left( \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \right)+\overline{d}h(T)\,\!</math>

The first term is estimated by:

:<math>{{\widehat{\lambda }}_{A}}=\frac{{{N}_{A}}}{T}=0.000077\,\!</math>

The second term is:

:<math>\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}=0.00038\,\!</math>

This estimates the growth potential failure intensity:

:<math>\begin{align}
{{\widehat{\gamma }}_{GP}}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \\
= & 0.00046
\end{align}\,\!</math>

To estimate the last term <math>\overline{d}h(T)\,\!</math> of the Crow Extended model, partition the data in the table into intervals. This partition consists of <math>D\,\!</math> successive intervals. The length of the <math>{{q}^{th}}\,\!</math> interval is <math>{{L}_{q}},\,\!</math> <math>\,q=1,2,\ldots ,D\,\!</math>. It is not required that the intervals be of the same length, but there should be several (e.g., at least 5) cycles per interval on average. Also, let <math>{{S}_{1}}={{L}_{1}},\,\!</math> <math>{{S}_{2}}={{L}_{1}}+{{L}_{2}},\ldots ,\,\!</math> etc. be the accumulated time through the <math>{{q}^{th}}\,\!</math> interval. For the <math>{{q}^{th}}\,\!</math> interval, note the number of distinct BD modes, <math>M{{I}_{q}}\,\!</math>, appearing for the first time, <math>q=1,2,\ldots ,D\,\!</math>. See the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped Data for Distinct BD Modes'''
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| <math>\text{MI}_{1}\,\!</math> || <math>\text{L}_{1}\,\!</math> || <math>\text{S}_{1}\,\!</math>
|-
|2|| <math>\text{MI}_{2}\,\!</math>|| <math>\text{L}_{2}\,\!</math>|| <math>\text{S}_{2}\,\!</math>
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|D|| <math>\text{MI}_{D}\,\!</math> || <math>\text{L}_{D}\,\!</math>|| <math>\text{S}_{D}\,\!</math>
|}

The term <math>\widehat{h}(T)\,\!</math> is calculated as <math>\widehat{h}(T)=\widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}}\,\!</math> and the values <math>\widehat{\lambda }\,\!</math> and <math>\widehat{\beta }\,\!</math> satisfy the maximum likelihood equations for grouped data (given in [[Fleet_Data_Analysis#Analyze_the_Grouped_Data|the Methodology section]]). This is the grouped data version of the Crow-AMSAA model applied only to the first occurrence of distinct BD modes.

For the data in the first table, the first 4 intervals had a length of 10,000 and the last interval was 12,110. Therefore, <math>D=5\,\!</math>. This choice gives an average of about 5 overhaul cycles per interval. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped Data for Distinct BD modes from [[Fleet_Data_Analysis#Applying_the_Crow_Extended_Model_to_Fleet_Data|Applying the Crow Extended Model to Fleet Data]]
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| 4|| 10000|| 10000
|-
|2|| 3|| 10000|| 20000
|-
|3|| 1|| 10000|| 30000
|-
|4|| 0|| 10000|| 40000
|-
|5|| 5|| 12110|| 52110
|-
|Total|| 13||
|}

Thus:

:<math>\begin{align}
\widehat{\lambda }= & 0.00330 \\
\widehat{\beta }= & 0.76219
\end{align}\,\!</math>

This gives:

:<math>\begin{align}
\widehat{h}(T)= & \widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}} \\
= & 0.00019
\end{align}\,\!</math>

Consequently, for <math>\overline{d}=0.4\,\!</math> the last term of the Crow Extended model is given by:

:<math>\overline{d}h(T)=0.000076\,\!</math>

The projected failure intensity is:

:<math>\begin{align}
\widehat{r}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}+\overline{d}h(T) \\
= & 0.000077+0.6\times (0.00063)+0.4\times (0.00019) \\
= & 0.000533
\end{align}\,\!</math>

This estimates that the 13 proposed corrective actions will reduce the number of failures per cycle of operation hours from the current <math>\widehat{r}(0)=\tfrac{{{N}_{A}}+{{N}_{BD}}}{T}=0.00071\,\!</math> to <math>\widehat{r}(T)=0.00053.\,\!</math> The average time between failures is estimated to increase from the current 1408.38 hours to 1876.93 hours.

==Confidence Bounds==
For fleet data analysis using the Crow-AMSAA model, the confidence bounds are calculated using the same procedure described for the Crow-AMSAA (NHPP) model (See [[Crow-AMSAA Confidence Bounds]]). For fleet data analysis using the Crow Extended model, the confidence bounds are calculated using the same procedure described for the Crow Extended model (See [[Crow Extended Confidence Bounds]]).

=More Examples=
==Predicting the Number of Failures for Fleet Operation==
{{:Crow_Extended_Model_Fleet_Analysis_Example}}

Crow Extended Model Fleet Analysis Example

2014-06-12T16:16:25Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Fleet_Data_Analysis|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

11 systems from the field were chosen for fleet analysis. Each system had at least one failure. All of the systems had a start time equal to zero and the last failure for each system corresponds to the end time. Group the data based on a fixed interval of 3,000 hours, and assume a fixed effectiveness factor equal to 0.4. Do the following:

#Estimate the parameters of the Crow Extended model.
#Based on the analysis, does it appear that the systems were randomly ordered?
#After the implementation of the delayed fixes, how many failures would you expect within the next 4,000 hours of fleet operation.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Fleet Data'''
|-
!System
!Times-to-Failure
|-
|1|| 1137 BD1, 1268 BD2
|-
|2|| 682 BD3, 744 A, 1336 BD1
|-
|3|| 95 BD1, 1593 BD3
|-
|4|| 1421 A
|-
|5|| 1091 A, 1574 BD2
|-
|6|| 1415 BD4
|-
|7|| 598 BD4, 1290 BD1
|-
|8|| 1556 BD5
|-
|9|| 55 BD4
|-
|10|| 730 BD1, 1124 BD3
|-
|11|| 1400 BD4, 1568 A
|}

'''Solution'''
<ol>
<li>The next figure shows the estimated Crow Extended parameters.

[[Image:rga13.8.png|center|600px]]
</li>
<li>Upon observing the estimated parameter <math>\beta \,\!</math>, it does appear that the systems were randomly ordered since <math>\beta =0.8569\,\!</math>. This value is close to 1. You can also verify that the confidence bounds on <math>\beta \,\!</math> include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.

[[Image:rga13.9.png|center|450px]]
</li>
<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.
[[Image:FleetExampleGPPlot.png|center|450px]]

To estimate the number of failures during the next 4,000 hours, calculate the following:

<math>\begin{align}
N=& \frac{4000}{1035.6802}\\
= & 3.8622\end{align}\,\!</math>

Therefore, it is estimated that <math>\approx\,\!</math> 4 failures will be observed during the next 4,000 hours of fleet operation.
</li>
</ol>

Fleet Data Analysis

2014-06-12T16:15:53Z

Chris Kahn:

{{template:RGA BOOK|6.3|Fleet Data Analysis}}
Fleet analysis is similar to the [[Repairable Systems Analysis|repairable systems analysis]] described in the previous chapter. The main difference is that a fleet of systems is considered and the models are applied to the fleet failures rather than to the system failures. In other words, repairable system analysis models the number of system failures versus system time, whereas fleet analysis models the number of fleet failures versus fleet time.
 

The main motivation for fleet analysis is to enable the application of the Crow Extended model for fielded data. In many cases, reliability improvements might be necessary on systems that are already in the field. These types of reliability improvements are essentially delayed fixes (BD modes) as described in the [[Crow Extended]] chapter.
 

==Introduction==
Recall from the previous chapter that in order to make projections using the [[Crow Extended]] model, the <math>\beta \,\!</math> of the combined A and BD modes should be equal to 1. Since the failure intensity in a fielded system might be changing over time (e.g., increasing if the system wears out), this assumption might be violated. In such a scenario, the Crow Extended model cannot be used. However, if a fleet of systems is considered and the number of fleet failures versus fleet time is modeled, the failures might become random. This is because there is a mixture of systems within a fleet, new and old, and when the failures of this mixture of systems are viewed from a cumulative fleet time point of view, they may be random. The next two figures illustrate this concept. The first picture shows the number of failures over system age. It can be clearly seen that as the systems age, the intensity of the failures increases (wearout). The superposition system line, which brings the failures from the different systems under a single timeline, also illustrates this observation. On the other hand, if you take the same four systems and combine their failures from a fleet perspective, and consider fleet failures over cumulative fleet hours, then the failures seem to be random. The second picture illustrates this concept in the System Operation plot when you consider the Cum. Time Line. In this case, the <math>\beta \,\!</math> of the fleet will be equal to 1 and the Crow Extended model can be used for quantifying the effects of future reliability improvements on the fleet.

[[Image:rga13.5.png|thumb|center|400px|Repairable System Operation plot.]]

[[Image:rga13.6.png|thumb|center|400px|Fleet System Operation plot.]]

==Methodology==
The figures above illustrate that the difference between repairable system data analysis and fleet analysis is the way that the data set is treated. In fleet analysis, the time-to-failure data from each system is stacked to a cumulative timeline. For example, consider the two systems in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"|'''System Data'''
|-
!System
!Failure Times (hr)
!End Time (hr)
|-
|1|| 3, 7|| 10
|-
|2|| 4, 9, 13|| 15
|}

===Convert to Accumulated Timeline===
The data set is first converted to an accumulated timeline, as follows:

*System 1 is considered first. The accumulated timeline is therefore 3 and 7 hours.
*System 1's end time is 10 hours. System 2's first failure is at 4 hours. This failure time is added to System 1's end time to give an accumulated failure time of 14 hours.
*The second failure for System 2 occurred 5 hours after the first failure. This time interval is added to the accumulated timeline to give 19 hours.
*The third failure for System 2 occurred 4 hours after the second failure. The accumulated failure time is 19 + 4 = 23 hours.
*System 2's end time is 15 hours, or 2 hours after the last failure. The total accumulated operating time for the fleet is 25 hours (23 + 2 = 25).

In general, the accumulated operating time <math>{{Y}_{j}}\,\!</math> is calculated by:

:<math>{{Y}_{j}}={{X}_{i,q}}+\underset{q=1}{\overset{K-1}{\mathop \sum }}\,{{T}_{q}},\text{ }m=1,2,...,N\,\!</math>

where:

*<math>{{X}_{i,q}}\,\!</math> is the <math>{{i}^{th}}\,\!</math> failure of the <math>{{q}^{th}}\,\!</math> system
*<math>{{T}_{q}}\,\!</math> is the end time of the <math>{{q}^{th}}\,\!</math> system
*<math>K\,\!</math> is the total number of systems
*<math>N\,\!</math> is the total number of failures from all systems ( <math>N=\underset{j=1}{\overset{K}{\mathop{\sum }}}\,{{N}_{q}}\,\!</math> )

As this example demonstrates, the accumulated timeline is determined based on the order of the systems. So if you consider the data in the table by taking System 2 first, the accumulated timeline would be: 4, 9, 13, 18, 22, with an end time of 25. Therefore, the order in which the systems are considered is somewhat important. However, in the next step of the analysis, the data from the accumulated timeline will be grouped into time intervals, effectively eliminating the importance of the order of the systems. Keep in mind that this will NOT always be true. This is true only when the order of the systems was random to begin with. If there is some logic/pattern in the order of the systems, then it will remain even if the cumulative timeline is converted to grouped data. For example, consider a system that wears out with age. This means that more failures will be observed as this system ages and these failures will occur more frequently. Within a fleet of such systems, there will be new and old systems in operation. If the data set collected is considered from the newest to the oldest system, then even if the data points are grouped, the pattern of fewer failures at the beginning and more failures at later time intervals will still be present. If the objective of the analysis is to determine the difference between newer and older systems, then that order for the data will be acceptable. However, if the objective of the analysis is to determine the reliability of the fleet, then the systems should be randomly ordered.

===Analyze the Grouped Data===
Once the accumulated timeline has been generated, it is then converted into grouped data. To accomplish this, a group interval is required. The group interval length should be chosen so that it is representative of the data. Also note that the intervals do not have to be of equal length. Once the data points have been grouped, the parameters can be obtained using maximum likelihood estimation as described in the [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP) chapter]]. The data from the table above can be grouped into 5 hour intervals. This interval length is sufficiently large to insure that there are failures within each interval. The grouped data set is given in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Grouped Data'''
|-
!Failures in Interval
!Interval End Time
|-
|1|| 5
|-
|1|| 10
|-
|1|| 15
|-
|1|| 20
|-
|1|| 25
|}

The Crow-AMSAA model for grouped failure times is used for the data, and the parameters of the model are solved by satisfying the following maximum likelihood equations (See [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP)]]):

:<math>\widehat{\lambda }=\frac{n}{T_{k}^{\widehat{\beta }}}\,\!</math>

:<math>\underset{i=1}{\overset{k}{\mathop \sum }}\,{{n}_{i}}\left[ \frac{T_{i}^{\widehat{\beta }}\ln {{T}_{i-1}}-T_{i-1}^{\widehat{\beta }}\ln {{T}_{i-1}}}{T_{i}^{\widehat{\beta }}-T_{i-1}^{\widehat{\beta }}}-\ln {{T}_{k}} \right]=0 </math>

==Fleet Analysis Example==
{{:Fleet_Analysis_Example}}

==Applying the Crow Extended Model to Fleet Data==
As it was mentioned previously, the main motivation of the fleet analysis is to apply the Crow Extended model for in-service reliability improvements. The methodology to be used is identical to the application of the [[Crow_Extended#Grouped_Data|Crow Extended model for Grouped Data]] described in a previous chapter. Consider the fleet data from the example above. In order to apply the Crow Extended model, put <math>N=37\,\!</math> failure times on a cumulative time scale over <math>(0,T)\,\!</math>, where <math>T=52110\,\!</math>. In the example, each <math>{{T}_{i}}\,\!</math> corresponds to a failure time <math>{{X}_{ij}}\,\!</math>. This is often not the situation. However, in all cases the accumulated operating time <math>{{Y}_{q}}\,\!</math> at a failure time <math>{{X}_{ir}}\,\!</math> is:

:<math>\begin{align}
{{Y}_{q}}= & {{X}_{i,r}}+\underset{j=1}{\overset{r-1}{\mathop \sum }}\,{{T}_{j}},\ \ \ q=1,2,\ldots ,N \\
N= & \underset{j=1}{\overset{K}{\mathop \sum }}\,{{N}_{j}}
\end{align}\,\!</math>

And <math>q\,\!</math> indexes the successive order of the failures. Thus, in this example <math>N=37,\,{{Y}_{1}}=1396,\,{{Y}_{2}}=5893,\,{{Y}_{3}}=6418,\ldots ,{{Y}_{37}}=52110\,\!</math>. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="7" style="text-align:center"|'''Test-Find-Test Fleet Data'''
|-
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
!
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
|-
|1|| 1396|| BD1|| || 20|| 26361|| BD1
|-
|2|| 5893|| BD2|| || 21|| 26392|| A
|-
|3|| 6418|| A|| || 22|| 26845|| BD8
|-
|4|| 7650|| BD3|| || 23|| 30477|| BD1
|-
|5|| 7877|| BD4|| || 24|| 31500|| A
|-
|6|| 8012|| BD2|| || 25|| 31661|| BD3
|-
|7|| 8031|| BD2|| || 26|| 31697|| BD2
|-
|8|| 8843|| BD1|| || 27|| 36428|| BD1
|-
|9|| 10867|| BD1|| || 28|| 40223|| BD1
|-
|10|| 11183|| BD5|| || 29|| 40803|| BD9
|-
|11|| 11810|| A|| || 30|| 42656|| BD1
|-
|12|| 11870|| BD1|| || 31|| 42724|| BD10
|-
|13|| 16139|| BD2|| || 32|| 44554|| BD1
|-
|14|| 16104|| BD6|| || 33|| 45795|| BD11
|-
|15|| 18178|| BD7|| || 34|| 46666|| BD12
|-
|16|| 18677|| BD2|| || 35|| 48368|| BD1
|-
|17|| 20751|| BD4|| || 36|| 51924|| BD13
|-
|18|| 20772|| BD2|| || 37|| 52110|| BD2
|-
|19|| 25815|| BD1|| || ||
|}

Each system failure time in the table above corresponds to a problem and a cause (failure mode). The management strategy can be to not fix the failure mode (A mode) or to fix the failure mode with a delayed corrective action (BD mode). There are <math>{{N}_{A}}=4\,\!</math> failures due to A failure modes. There are <math>{{N}_{BD}}=33\,\!</math> total failures due to <math>M=13\,\!</math> distinct BD failure modes. Some of the distinct BD modes had repeats of the same problem. For example, mode BD1 had 12 occurrences of the same problem. Therefore, in this example, there are 13 distinct corrective actions corresponding to 13 distinct BD failure modes.

The objective of the Crow Extended model is to estimate the impact of the 13 distinct corrective actions.The analyst will choose an average effectiveness factor (EF) based on the proposed corrective actions and historical experience. Historical industry and government data supports a typical average effectiveness factor <math>\overline{d}=.70\,\!</math> for many systems. In this example, an average EF of <math>\bar{d}=0.4\,\!</math> was assumed in order to be conservative regarding the impact of the proposed corrective actions. Since there are no BC failure modes (corrective actions applied during the test), the projected failure intensity is:

:<math>\widehat{r}(T)=\left( \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \right)+\overline{d}h(T)\,\!</math>

The first term is estimated by:

:<math>{{\widehat{\lambda }}_{A}}=\frac{{{N}_{A}}}{T}=0.000077\,\!</math>

The second term is:

:<math>\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}=0.00038\,\!</math>

This estimates the growth potential failure intensity:

:<math>\begin{align}
{{\widehat{\gamma }}_{GP}}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \\
= & 0.00046
\end{align}\,\!</math>

To estimate the last term <math>\overline{d}h(T)\,\!</math> of the Crow Extended model, partition the data in the table into intervals. This partition consists of <math>D\,\!</math> successive intervals. The length of the <math>{{q}^{th}}\,\!</math> interval is <math>{{L}_{q}},\,\!</math> <math>\,q=1,2,\ldots ,D\,\!</math>. It is not required that the intervals be of the same length, but there should be several (e.g., at least 5) cycles per interval on average. Also, let <math>{{S}_{1}}={{L}_{1}},\,\!</math> <math>{{S}_{2}}={{L}_{1}}+{{L}_{2}},\ldots ,\,\!</math> etc. be the accumulated time through the <math>{{q}^{th}}\,\!</math> interval. For the <math>{{q}^{th}}\,\!</math> interval, note the number of distinct BD modes, <math>M{{I}_{q}}\,\!</math>, appearing for the first time, <math>q=1,2,\ldots ,D\,\!</math>. See the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped Data for Distinct BD Modes'''
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| <math>\text{MI}_{1}\,\!</math> || <math>\text{L}_{1}\,\!</math> || <math>\text{S}_{1}\,\!</math>
|-
|2|| <math>\text{MI}_{2}\,\!</math>|| <math>\text{L}_{2}\,\!</math>|| <math>\text{S}_{2}\,\!</math>
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|D|| <math>\text{MI}_{D}\,\!</math> || <math>\text{L}_{D}\,\!</math>|| <math>\text{S}_{D}\,\!</math>
|}

The term <math>\widehat{h}(T)\,\!</math> is calculated as <math>\widehat{h}(T)=\widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}}\,\!</math> and the values <math>\widehat{\lambda }\,\!</math> and <math>\widehat{\beta }\,\!</math> satisfy the maximum likelihood equations for grouped data (given in [[Fleet_Data_Analysis#Analyze_the_Grouped_Data|the Methodology section]]). This is the grouped data version of the Crow-AMSAA model applied only to the first occurrence of distinct BD modes.

For the data in the first table, the first 4 intervals had a length of 10,000 and the last interval was 12,110. Therefore, <math>D=5\,\!</math>. This choice gives an average of about 5 overhaul cycles per interval. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped Data for Distinct BD modes from [[Fleet_Data_Analysis#Applying_the_Crow_Extended_Model_to_Fleet_Data|Applying the Crow Extended Model to Fleet Data]]
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| 4|| 10000|| 10000
|-
|2|| 3|| 10000|| 20000
|-
|3|| 1|| 10000|| 30000
|-
|4|| 0|| 10000|| 40000
|-
|5|| 5|| 12110|| 52110
|-
|Total|| 13||
|}

Thus:

:<math>\begin{align}
\widehat{\lambda }= & 0.00330 \\
\widehat{\beta }= & 0.76219
\end{align}\,\!</math>

This gives:

:<math>\begin{align}
\widehat{h}(T)= & \widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}} \\
= & 0.00019
\end{align}\,\!</math>

Consequently, for <math>\overline{d}=0.4\,\!</math> the last term of the Crow Extended model is given by:

:<math>\overline{d}h(T)=0.000076\,\!</math>

The projected failure intensity is:

:<math>\begin{align}
\widehat{r}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}+\overline{d}h(T) \\
= & 0.000077+0.6\times (0.00063)+0.4\times (0.00019) \\
= & 0.000533
\end{align}\,\!</math>

This estimates that the 13 proposed corrective actions will reduce the number of failures per cycle of operation hours from the current <math>\widehat{r}(0)=\tfrac{{{N}_{A}}+{{N}_{BD}}}{T}=0.00071\,\!</math> to <math>\widehat{r}(T)=0.00053.\,\!</math> The average time between failures is estimated to increase from the current 1408.38 hours to 1876.93 hours.

==Confidence Bounds==
For fleet data analysis using the Crow-AMSAA model, the confidence bounds are calculated using the same procedure described for the Crow-AMSAA (NHPP) model (See [[Crow-AMSAA Confidence Bounds]]). For fleet data analysis using the Crow Extended model, the confidence bounds are calculated using the same procedure described for the Crow Extended model (See [[Crow Extended Confidence Bounds]]).

=More Examples=
==Predicting the Number of Failures for Fleet Operation==
{{:Crow_Extended_Model_Fleet_Analysis_Example}}

Fleet Data Analysis

2014-06-12T15:41:33Z

Chris Kahn: /* Applying the Crow Extended Model to Fleet Data */

{{template:RGA BOOK|6.3|Fleet Data Analysis}}
Fleet analysis is similar to the [[Repairable Systems Analysis|repairable systems analysis]] described in the previous chapter. The main difference is that a fleet of systems is considered and the models are applied to the fleet failures rather than to the system failures. In other words, repairable system analysis models the number of system failures versus system time, whereas fleet analysis models the number of fleet failures versus fleet time.
 

The main motivation for fleet analysis is to enable the application of the Crow Extended model for fielded data. In many cases, reliability improvements might be necessary on systems that are already in the field. These types of reliability improvements are essentially delayed fixes (BD modes) as described in the [[Crow Extended]] chapter.
 

==Introduction==
Recall from the previous chapter that in order to make projections using the [[Crow Extended]] model, the <math>\beta \,\!</math> of the combined A and BD modes should be equal to 1. Since the failure intensity in a fielded system might be changing over time (e.g., increasing if the system wears out), this assumption might be violated. In such a scenario, the Crow Extended model cannot be used. However, if a fleet of systems is considered and the number of fleet failures versus fleet time is modeled, the failures might become random. This is because there is a mixture of systems within a fleet, new and old, and when the failures of this mixture of systems are viewed from a cumulative fleet time point of view, they may be random. The next two figures illustrate this concept. The first picture shows the number of failures over system age. It can be clearly seen that as the systems age, the intensity of the failures increases (wearout). The superposition system line, which brings the failures from the different systems under a single timeline, also illustrates this observation. On the other hand, if you take the same four systems and combine their failures from a fleet perspective, and consider fleet failures over cumulative fleet hours, then the failures seem to be random. The second picture illustrates this concept in the System Operation plot when you consider the Cum. Time Line. In this case, the <math>\beta \,\!</math> of the fleet will be equal to 1 and the Crow Extended model can be used for quantifying the effects of future reliability improvements on the fleet.

[[Image:rga13.5.png|thumb|center|400px|Repairable System Operation plot.]]

[[Image:rga13.6.png|thumb|center|400px|Fleet System Operation plot.]]

==Methodology==
The figures above illustrate that the difference between repairable system data analysis and fleet analysis is the way that the data set is treated. In fleet analysis, the time-to-failure data from each system is stacked to a cumulative timeline. For example, consider the two systems in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"|'''System Data'''
|-
!System
!Failure Times (hr)
!End Time (hr)
|-
|1|| 3, 7|| 10
|-
|2|| 4, 9, 13|| 15
|}

===Convert to Accumulated Timeline===
The data set is first converted to an accumulated timeline, as follows:

*System 1 is considered first. The accumulated timeline is therefore 3 and 7 hours.
*System 1's end time is 10 hours. System 2's first failure is at 4 hours. This failure time is added to System 1's end time to give an accumulated failure time of 14 hours.
*The second failure for System 2 occurred 5 hours after the first failure. This time interval is added to the accumulated timeline to give 19 hours.
*The third failure for System 2 occurred 4 hours after the second failure. The accumulated failure time is 19 + 4 = 23 hours.
*System 2's end time is 15 hours, or 2 hours after the last failure. The total accumulated operating time for the fleet is 25 hours (23 + 2 = 25).

In general, the accumulated operating time <math>{{Y}_{j}}\,\!</math> is calculated by:

:<math>{{Y}_{j}}={{X}_{i,q}}+\underset{q=1}{\overset{K-1}{\mathop \sum }}\,{{T}_{q}},\text{ }m=1,2,...,N\,\!</math>

where:

*<math>{{X}_{i,q}}\,\!</math> is the <math>{{i}^{th}}\,\!</math> failure of the <math>{{q}^{th}}\,\!</math> system
*<math>{{T}_{q}}\,\!</math> is the end time of the <math>{{q}^{th}}\,\!</math> system
*<math>K\,\!</math> is the total number of systems
*<math>N\,\!</math> is the total number of failures from all systems ( <math>N=\underset{j=1}{\overset{K}{\mathop{\sum }}}\,{{N}_{q}}\,\!</math> )

As this example demonstrates, the accumulated timeline is determined based on the order of the systems. So if you consider the data in the table by taking System 2 first, the accumulated timeline would be: 4, 9, 13, 18, 22, with an end time of 25. Therefore, the order in which the systems are considered is somewhat important. However, in the next step of the analysis, the data from the accumulated timeline will be grouped into time intervals, effectively eliminating the importance of the order of the systems. Keep in mind that this will NOT always be true. This is true only when the order of the systems was random to begin with. If there is some logic/pattern in the order of the systems, then it will remain even if the cumulative timeline is converted to grouped data. For example, consider a system that wears out with age. This means that more failures will be observed as this system ages and these failures will occur more frequently. Within a fleet of such systems, there will be new and old systems in operation. If the data set collected is considered from the newest to the oldest system, then even if the data points are grouped, the pattern of fewer failures at the beginning and more failures at later time intervals will still be present. If the objective of the analysis is to determine the difference between newer and older systems, then that order for the data will be acceptable. However, if the objective of the analysis is to determine the reliability of the fleet, then the systems should be randomly ordered.

===Analyze the Grouped Data===
Once the accumulated timeline has been generated, it is then converted into grouped data. To accomplish this, a group interval is required. The group interval length should be chosen so that it is representative of the data. Also note that the intervals do not have to be of equal length. Once the data points have been grouped, the parameters can be obtained using maximum likelihood estimation as described in the [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP) chapter]]. The data from the table above can be grouped into 5 hour intervals. This interval length is sufficiently large to insure that there are failures within each interval. The grouped data set is given in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Grouped Data'''
|-
!Failures in Interval
!Interval End Time
|-
|1|| 5
|-
|1|| 10
|-
|1|| 15
|-
|1|| 20
|-
|1|| 25
|}

The Crow-AMSAA model for grouped failure times is used for the data, and the parameters of the model are solved by satisfying the following maximum likelihood equations (See [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP)]]):

:<math>\widehat{\lambda }=\frac{n}{T_{k}^{\widehat{\beta }}}\,\!</math>

:<math>\underset{i=1}{\overset{k}{\mathop \sum }}\,{{n}_{i}}\left[ \frac{T_{i}^{\widehat{\beta }}\ln {{T}_{i-1}}-T_{i-1}^{\widehat{\beta }}\ln {{T}_{i-1}}}{T_{i}^{\widehat{\beta }}-T_{i-1}^{\widehat{\beta }}}-\ln {{T}_{k}} \right]=0 </math>

==Fleet Analysis Example==
{{:Fleet_Analysis_Example}}

==Applying the Crow Extended Model to Fleet Data==
As it was mentioned previously, the main motivation of the fleet analysis is to apply the Crow Extended model for in-service reliability improvements. The methodology to be used is identical to the application of the [[Crow_Extended#Grouped_Data|Crow Extended model for Grouped Data]] described in a previous chapter. Consider the fleet data from the example above. In order to apply the Crow Extended model, put <math>N=37\,\!</math> failure times on a cumulative time scale over <math>(0,T)\,\!</math>, where <math>T=52110\,\!</math>. In the example, each <math>{{T}_{i}}\,\!</math> corresponds to a failure time <math>{{X}_{ij}}\,\!</math>. This is often not the situation. However, in all cases the accumulated operating time <math>{{Y}_{q}}\,\!</math> at a failure time <math>{{X}_{ir}}\,\!</math> is:

:<math>\begin{align}
{{Y}_{q}}= & {{X}_{i,r}}+\underset{j=1}{\overset{r-1}{\mathop \sum }}\,{{T}_{j}},\ \ \ q=1,2,\ldots ,N \\
N= & \underset{j=1}{\overset{K}{\mathop \sum }}\,{{N}_{j}}
\end{align}\,\!</math>

And <math>q\,\!</math> indexes the successive order of the failures. Thus, in this example <math>N=37,\,{{Y}_{1}}=1396,\,{{Y}_{2}}=5893,\,{{Y}_{3}}=6418,\ldots ,{{Y}_{37}}=52110\,\!</math>. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="7" style="text-align:center"|'''Test-Find-Test Fleet Data'''
|-
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
!
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
|-
|1|| 1396|| BD1|| || 20|| 26361|| BD1
|-
|2|| 5893|| BD2|| || 21|| 26392|| A
|-
|3|| 6418|| A|| || 22|| 26845|| BD8
|-
|4|| 7650|| BD3|| || 23|| 30477|| BD1
|-
|5|| 7877|| BD4|| || 24|| 31500|| A
|-
|6|| 8012|| BD2|| || 25|| 31661|| BD3
|-
|7|| 8031|| BD2|| || 26|| 31697|| BD2
|-
|8|| 8843|| BD1|| || 27|| 36428|| BD1
|-
|9|| 10867|| BD1|| || 28|| 40223|| BD1
|-
|10|| 11183|| BD5|| || 29|| 40803|| BD9
|-
|11|| 11810|| A|| || 30|| 42656|| BD1
|-
|12|| 11870|| BD1|| || 31|| 42724|| BD10
|-
|13|| 16139|| BD2|| || 32|| 44554|| BD1
|-
|14|| 16104|| BD6|| || 33|| 45795|| BD11
|-
|15|| 18178|| BD7|| || 34|| 46666|| BD12
|-
|16|| 18677|| BD2|| || 35|| 48368|| BD1
|-
|17|| 20751|| BD4|| || 36|| 51924|| BD13
|-
|18|| 20772|| BD2|| || 37|| 52110|| BD2
|-
|19|| 25815|| BD1|| || ||
|}

Each system failure time in the table above corresponds to a problem and a cause (failure mode). The management strategy can be to not fix the failure mode (A mode) or to fix the failure mode with a delayed corrective action (BD mode). There are <math>{{N}_{A}}=4\,\!</math> failures due to A failure modes. There are <math>{{N}_{BD}}=33\,\!</math> total failures due to <math>M=13\,\!</math> distinct BD failure modes. Some of the distinct BD modes had repeats of the same problem. For example, mode BD1 had 12 occurrences of the same problem. Therefore, in this example, there are 13 distinct corrective actions corresponding to 13 distinct BD failure modes.

The objective of the Crow Extended model is to estimate the impact of the 13 distinct corrective actions.The analyst will choose an average effectiveness factor (EF) based on the proposed corrective actions and historical experience. Historical industry and government data supports a typical average effectiveness factor <math>\overline{d}=.70\,\!</math> for many systems. In this example, an average EF of <math>\bar{d}=0.4\,\!</math> was assumed in order to be conservative regarding the impact of the proposed corrective actions. Since there are no BC failure modes (corrective actions applied during the test), the projected failure intensity is:

:<math>\widehat{r}(T)=\left( \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \right)+\overline{d}h(T)\,\!</math>

The first term is estimated by:

:<math>{{\widehat{\lambda }}_{A}}=\frac{{{N}_{A}}}{T}=0.000077\,\!</math>

The second term is:

:<math>\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}=0.00038\,\!</math>

This estimates the growth potential failure intensity:

:<math>\begin{align}
{{\widehat{\gamma }}_{GP}}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \\
= & 0.00046
\end{align}\,\!</math>

To estimate the last term <math>\overline{d}h(T)\,\!</math> of the Crow Extended model, partition the data in the table into intervals. This partition consists of <math>D\,\!</math> successive intervals. The length of the <math>{{q}^{th}}\,\!</math> interval is <math>{{L}_{q}},\,\!</math> <math>\,q=1,2,\ldots ,D\,\!</math>. It is not required that the intervals be of the same length, but there should be several (e.g., at least 5) cycles per interval on average. Also, let <math>{{S}_{1}}={{L}_{1}},\,\!</math> <math>{{S}_{2}}={{L}_{1}}+{{L}_{2}},\ldots ,\,\!</math> etc. be the accumulated time through the <math>{{q}^{th}}\,\!</math> interval. For the <math>{{q}^{th}}\,\!</math> interval, note the number of distinct BD modes, <math>M{{I}_{q}}\,\!</math>, appearing for the first time, <math>q=1,2,\ldots ,D\,\!</math>. See the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped Data for Distinct BD Modes'''
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| <math>\text{MI}_{1}\,\!</math> || <math>\text{L}_{1}\,\!</math> || <math>\text{S}_{1}\,\!</math>
|-
|2|| <math>\text{MI}_{2}\,\!</math>|| <math>\text{L}_{2}\,\!</math>|| <math>\text{S}_{2}\,\!</math>
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|D|| <math>\text{MI}_{D}\,\!</math> || <math>\text{L}_{D}\,\!</math>|| <math>\text{S}_{D}\,\!</math>
|}

The term <math>\widehat{h}(T)\,\!</math> is calculated as <math>\widehat{h}(T)=\widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}}\,\!</math> and the values <math>\widehat{\lambda }\,\!</math> and <math>\widehat{\beta }\,\!</math> satisfy the maximum likelihood equations for grouped data (given in [[Fleet_Data_Analysis#Analyze_the_Grouped_Data|the Methodology section]]). This is the grouped data version of the Crow-AMSAA model applied only to the first occurrence of distinct BD modes.

For the data in the first table, the first 4 intervals had a length of 10,000 and the last interval was 12,110. Therefore, <math>D=5\,\!</math>. This choice gives an average of about 5 overhaul cycles per interval. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped data for distinct BD modes from Table 13.6'''
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| 4|| 10000|| 10000
|-
|2|| 3|| 10000|| 20000
|-
|3|| 1|| 10000|| 30000
|-
|4|| 0|| 10000|| 40000
|-
|5|| 5|| 12110|| 52110
|-
|Total|| 13||
|}

Thus:

:<math>\begin{align}
\widehat{\lambda }= & 0.00330 \\
\widehat{\beta }= & 0.76219
\end{align}\,\!</math>

This gives:

:<math>\begin{align}
\widehat{h}(T)= & \widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}} \\
= & 0.00019
\end{align}\,\!</math>

Consequently, for <math>\overline{d}=0.4\,\!</math> the last term of the Crow Extended model is given by:

:<math>\overline{d}h(T)=0.000076\,\!</math>

The projected failure intensity is:

:<math>\begin{align}
\widehat{r}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}+\overline{d}h(T) \\
= & 0.000077+0.6\times (0.00063)+0.4\times (0.00019) \\
= & 0.000533
\end{align}\,\!</math>

This estimates that the 13 proposed corrective actions will reduce the number of failures per cycle of operation hours from the current <math>\widehat{r}(0)=\tfrac{{{N}_{A}}+{{N}_{BD}}}{T}=0.00071\,\!</math> to <math>\widehat{r}(T)=0.00053.\,\!</math> The average time between failures is estimated to increase from the current 1408.38 hours to 1876.93 hours.

==Confidence Bounds==
For fleet data analysis using the Crow-AMSAA model, the confidence bounds are calculated using the same procedure described for the Crow-AMSAA (NHPP) model (See [[Crow-AMSAA Confidence Bounds]]). For fleet data analysis using the Crow Extended model, the confidence bounds are calculated using the same procedure described for the Crow Extended model (See [[Crow Extended Confidence Bounds]]).

=More Examples=
==Predicting the Number of Failures for Fleet Operation==
{{:Crow_Extended_Model_Fleet_Analysis_Example}}

Fleet Data Analysis

2014-06-12T15:34:20Z

Chris Kahn: /* Applying the Crow Extended Model to Fleet Data */

{{template:RGA BOOK|6.3|Fleet Data Analysis}}
Fleet analysis is similar to the [[Repairable Systems Analysis|repairable systems analysis]] described in the previous chapter. The main difference is that a fleet of systems is considered and the models are applied to the fleet failures rather than to the system failures. In other words, repairable system analysis models the number of system failures versus system time, whereas fleet analysis models the number of fleet failures versus fleet time.
 

The main motivation for fleet analysis is to enable the application of the Crow Extended model for fielded data. In many cases, reliability improvements might be necessary on systems that are already in the field. These types of reliability improvements are essentially delayed fixes (BD modes) as described in the [[Crow Extended]] chapter.
 

==Introduction==
Recall from the previous chapter that in order to make projections using the [[Crow Extended]] model, the <math>\beta \,\!</math> of the combined A and BD modes should be equal to 1. Since the failure intensity in a fielded system might be changing over time (e.g., increasing if the system wears out), this assumption might be violated. In such a scenario, the Crow Extended model cannot be used. However, if a fleet of systems is considered and the number of fleet failures versus fleet time is modeled, the failures might become random. This is because there is a mixture of systems within a fleet, new and old, and when the failures of this mixture of systems are viewed from a cumulative fleet time point of view, they may be random. The next two figures illustrate this concept. The first picture shows the number of failures over system age. It can be clearly seen that as the systems age, the intensity of the failures increases (wearout). The superposition system line, which brings the failures from the different systems under a single timeline, also illustrates this observation. On the other hand, if you take the same four systems and combine their failures from a fleet perspective, and consider fleet failures over cumulative fleet hours, then the failures seem to be random. The second picture illustrates this concept in the System Operation plot when you consider the Cum. Time Line. In this case, the <math>\beta \,\!</math> of the fleet will be equal to 1 and the Crow Extended model can be used for quantifying the effects of future reliability improvements on the fleet.

[[Image:rga13.5.png|thumb|center|400px|Repairable System Operation plot.]]

[[Image:rga13.6.png|thumb|center|400px|Fleet System Operation plot.]]

==Methodology==
The figures above illustrate that the difference between repairable system data analysis and fleet analysis is the way that the data set is treated. In fleet analysis, the time-to-failure data from each system is stacked to a cumulative timeline. For example, consider the two systems in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"|'''System Data'''
|-
!System
!Failure Times (hr)
!End Time (hr)
|-
|1|| 3, 7|| 10
|-
|2|| 4, 9, 13|| 15
|}

===Convert to Accumulated Timeline===
The data set is first converted to an accumulated timeline, as follows:

*System 1 is considered first. The accumulated timeline is therefore 3 and 7 hours.
*System 1's end time is 10 hours. System 2's first failure is at 4 hours. This failure time is added to System 1's end time to give an accumulated failure time of 14 hours.
*The second failure for System 2 occurred 5 hours after the first failure. This time interval is added to the accumulated timeline to give 19 hours.
*The third failure for System 2 occurred 4 hours after the second failure. The accumulated failure time is 19 + 4 = 23 hours.
*System 2's end time is 15 hours, or 2 hours after the last failure. The total accumulated operating time for the fleet is 25 hours (23 + 2 = 25).

In general, the accumulated operating time <math>{{Y}_{j}}\,\!</math> is calculated by:

:<math>{{Y}_{j}}={{X}_{i,q}}+\underset{q=1}{\overset{K-1}{\mathop \sum }}\,{{T}_{q}},\text{ }m=1,2,...,N\,\!</math>

where:

*<math>{{X}_{i,q}}\,\!</math> is the <math>{{i}^{th}}\,\!</math> failure of the <math>{{q}^{th}}\,\!</math> system
*<math>{{T}_{q}}\,\!</math> is the end time of the <math>{{q}^{th}}\,\!</math> system
*<math>K\,\!</math> is the total number of systems
*<math>N\,\!</math> is the total number of failures from all systems ( <math>N=\underset{j=1}{\overset{K}{\mathop{\sum }}}\,{{N}_{q}}\,\!</math> )

As this example demonstrates, the accumulated timeline is determined based on the order of the systems. So if you consider the data in the table by taking System 2 first, the accumulated timeline would be: 4, 9, 13, 18, 22, with an end time of 25. Therefore, the order in which the systems are considered is somewhat important. However, in the next step of the analysis, the data from the accumulated timeline will be grouped into time intervals, effectively eliminating the importance of the order of the systems. Keep in mind that this will NOT always be true. This is true only when the order of the systems was random to begin with. If there is some logic/pattern in the order of the systems, then it will remain even if the cumulative timeline is converted to grouped data. For example, consider a system that wears out with age. This means that more failures will be observed as this system ages and these failures will occur more frequently. Within a fleet of such systems, there will be new and old systems in operation. If the data set collected is considered from the newest to the oldest system, then even if the data points are grouped, the pattern of fewer failures at the beginning and more failures at later time intervals will still be present. If the objective of the analysis is to determine the difference between newer and older systems, then that order for the data will be acceptable. However, if the objective of the analysis is to determine the reliability of the fleet, then the systems should be randomly ordered.

===Analyze the Grouped Data===
Once the accumulated timeline has been generated, it is then converted into grouped data. To accomplish this, a group interval is required. The group interval length should be chosen so that it is representative of the data. Also note that the intervals do not have to be of equal length. Once the data points have been grouped, the parameters can be obtained using maximum likelihood estimation as described in the [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP) chapter]]. The data from the table above can be grouped into 5 hour intervals. This interval length is sufficiently large to insure that there are failures within each interval. The grouped data set is given in the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Grouped Data'''
|-
!Failures in Interval
!Interval End Time
|-
|1|| 5
|-
|1|| 10
|-
|1|| 15
|-
|1|| 20
|-
|1|| 25
|}

The Crow-AMSAA model for grouped failure times is used for the data, and the parameters of the model are solved by satisfying the following maximum likelihood equations (See [[Crow-AMSAA (NHPP)#Grouped_Data|Crow-AMSAA (NHPP)]]):

:<math>\widehat{\lambda }=\frac{n}{T_{k}^{\widehat{\beta }}}\,\!</math>

:<math>\underset{i=1}{\overset{k}{\mathop \sum }}\,{{n}_{i}}\left[ \frac{T_{i}^{\widehat{\beta }}\ln {{T}_{i-1}}-T_{i-1}^{\widehat{\beta }}\ln {{T}_{i-1}}}{T_{i}^{\widehat{\beta }}-T_{i-1}^{\widehat{\beta }}}-\ln {{T}_{k}} \right]=0 </math>

==Fleet Analysis Example==
{{:Fleet_Analysis_Example}}

==Applying the Crow Extended Model to Fleet Data==
As it was mentioned previously, the main motivation of the fleet analysis is to apply the Crow Extended model for in-service reliability improvements. The methodology to be used is identical to the application of the [[Crow_Extended#Grouped_Data|Crow Extended model for Grouped Data]] described in a previous chapter. Consider the fleet data from the example above. In order to apply the Crow Extended model, put <math>N=37\,\!</math> failure times on a cumulative time scale over <math>(0,T)\,\!</math>, where <math>T=52110\,\!</math>. In the example, each <math>{{T}_{i}}\,\!</math> corresponds to a failure time <math>{{X}_{ij}}\,\!</math>. This is often not the situation. However, in all cases the accumulated operating time <math>{{Y}_{q}}\,\!</math> at a failure time <math>{{X}_{ir}}\,\!</math> is:

:<math>\begin{align}
{{Y}_{q}}= & {{X}_{i,r}}+\underset{j=1}{\overset{r-1}{\mathop \sum }}\,{{T}_{j}},\ \ \ q=1,2,\ldots ,N \\
N= & \underset{j=1}{\overset{K}{\mathop \sum }}\,{{N}_{j}}
\end{align}\,\!</math>

And <math>q\,\!</math> indexes the successive order of the failures. Thus, in this example <math>N=37,\,{{Y}_{1}}=1396,\,{{Y}_{2}}=5893,\,{{Y}_{3}}=6418,\ldots ,{{Y}_{37}}=52110\,\!</math>. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="7" style="text-align:center"|'''Test-Find-Test Fleet Data'''
|-
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
!
!<math>q\,\!</math>
!<math>{{Y}_{q}}\,\!</math>
!Mode
|-
|1|| 1396|| BD1|| || 20|| 26361|| BD1
|-
|2|| 5893|| BD2|| || 21|| 26392|| A
|-
|3|| 6418|| A|| || 22|| 26845|| BD8
|-
|4|| 7650|| BD3|| || 23|| 30477|| BD1
|-
|5|| 7877|| BD4|| || 24|| 31500|| A
|-
|6|| 8012|| BD2|| || 25|| 31661|| BD3
|-
|7|| 8031|| BD2|| || 26|| 31697|| BD2
|-
|8|| 8843|| BD1|| || 27|| 36428|| BD1
|-
|9|| 10867|| BD1|| || 28|| 40223|| BD1
|-
|10|| 11183|| BD5|| || 29|| 40803|| BD9
|-
|11|| 11810|| A|| || 30|| 42656|| BD1
|-
|12|| 11870|| BD1|| || 31|| 42724|| BD10
|-
|13|| 16139|| BD2|| || 32|| 44554|| BD1
|-
|14|| 16104|| BD6|| || 33|| 45795|| BD11
|-
|15|| 18178|| BD7|| || 34|| 46666|| BD12
|-
|16|| 18677|| BD2|| || 35|| 48368|| BD1
|-
|17|| 20751|| BD4|| || 36|| 51924|| BD13
|-
|18|| 20772|| BD2|| || 37|| 52110|| BD2
|-
|19|| 25815|| BD1|| || ||
|}

Each system failure time in the table above corresponds to a problem and a cause (failure mode). The management strategy can be to not fix the failure mode (A mode) or to fix the failure mode with a delayed corrective action (BD mode). There are <math>{{N}_{A}}=4\,\!</math> failures due to A failure modes. There are <math>{{N}_{BD}}=33\,\!</math> total failures due to <math>M=13\,\!</math> distinct BD failure modes. Some of the distinct BD modes had repeats of the same problem. For example, mode BD1 had 12 occurrences of the same problem. Therefore, in this example, there are 13 distinct corrective actions corresponding to 13 distinct BD failure modes.

The objective of the Crow Extended model is to estimate the impact of the 13 distinct corrective actions.The analyst will choose an average effectiveness factor (EF) based on the proposed corrective actions and historical experience. Historical industry and government data supports a typical average effectiveness factor <math>\overline{d}=.70\,\!</math> for many systems. In this example, an average EF of <math>\bar{d}=0.4\,\!</math> was assumed in order to be conservative regarding the impact of the proposed corrective actions. Since there are no BC failure modes (corrective actions applied during the test), the projected failure intensity is:

:<math>\widehat{r}(T)=\left( \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \right)+\overline{d}h(T)\,\!</math>

The first term is estimated by:

:<math>{{\widehat{\lambda }}_{A}}=\frac{{{N}_{A}}}{T}=0.000077\,\!</math>

The second term is:

:<math>\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}=0.00038\,\!</math>

This estimates the growth potential failure intensity:

:<math>\begin{align}
{{\widehat{\gamma }}_{GP}}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T} \\
= & 0.00046
\end{align}\,\!</math>

To estimate the last term <math>\overline{d}h(T)\,\!</math> of the Crow Extended model, partition the data in the table into intervals. This partition consists of <math>D\,\!</math> successive intervals. The length of the <math>{{q}^{th}}\,\!</math> interval is <math>{{L}_{q}},\,\!</math> <math>\,q=1,2,\ldots ,D\,\!</math>. It is not required that the intervals be of the same length, but there should be several (e.g., at least 5) cycles per interval on average. Also, let <math>{{S}_{1}}={{L}_{1}},\,\!</math> <math>{{S}_{2}}={{L}_{1}}+{{L}_{2}},\ldots ,\,\!</math> etc. be the accumulated time through the <math>{{q}^{th}}\,\!</math> interval. For the <math>{{q}^{th}}\,\!</math> interval, note the number of distinct BD modes, <math>M{{I}_{q}}\,\!</math>, appearing for the first time, <math>q=1,2,\ldots ,D\,\!</math>. See the following table.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped data for distinct BD modes'''
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| <math>\text{MI}_{1}\,\!</math> || <math>\text{L}_{1}\,\!</math> || <math>\text{S}_{1}\,\!</math>
|-
|2|| <math>\text{MI}_{2}\,\!</math>|| <math>\text{L}_{2}\,\!</math>|| <math>\text{S}_{2}\,\!</math>
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|.|| .|| .|| .
|-
|D|| <math>\text{MI}_{D}\,\!</math> || <math>\text{L}_{D}\,\!</math>|| <math>\text{S}_{D}\,\!</math>
|}

The term <math>\widehat{h}(T)\,\!</math> is calculated as <math>\widehat{h}(T)=\widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}}\,\!</math> and the values <math>\widehat{\lambda }\,\!</math> and <math>\widehat{\beta }\,\!</math> satisfy the maximum likelihood equations for grouped data (given in [[Fleet_Data_Analysis#Analyze_the_Grouped_Data|the Methodology section]]). This is the grouped data version of the Crow-AMSAA model applied only to the first occurrence of distinct BD modes.

For the data in the first table, the first 4 intervals had a length of 10,000 and the last interval was 12,110. Therefore, <math>D=5\,\!</math>. This choice gives an average of about 5 overhaul cycles per interval. See the table below.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Grouped data for distinct BD modes from Table 13.6'''
|-
!Interval
!No. of Distinct BD Mode Failures
!Length
!Accumulated Time
|-
|1|| 4|| 10000|| 10000
|-
|2|| 3|| 10000|| 20000
|-
|3|| 1|| 10000|| 30000
|-
|4|| 0|| 10000|| 40000
|-
|5|| 5|| 12110|| 52110
|-
|Total|| 13||
|}

Thus:

:<math>\begin{align}
\widehat{\lambda }= & 0.00330 \\
\widehat{\beta }= & 0.76219
\end{align}\,\!</math>

This gives:

:<math>\begin{align}
\widehat{h}(T)= & \widehat{\lambda }\widehat{\beta }{{T}^{\widehat{\beta }-1}} \\
= & 0.00019
\end{align}\,\!</math>

Consequently, for <math>\overline{d}=0.4\,\!</math> the last term of the Crow Extended model is given by:

:<math>\overline{d}h(T)=0.000076\,\!</math>

The projected failure intensity is:

:<math>\begin{align}
\widehat{r}(T)= & \frac{{{N}_{A}}}{T}+\underset{i=1}{\overset{M}{\mathop \sum }}\,(1-{{d}_{i}})\frac{{{N}_{i}}}{T}+\overline{d}h(T) \\
= & 0.000077+0.6\times (0.00063)+0.4\times (0.00019) \\
= & 0.000533
\end{align}\,\!</math>

This estimates that the 13 proposed corrective actions will reduce the number of failures per cycle of operation hours from the current <math>\widehat{r}(0)=\tfrac{{{N}_{A}}+{{N}_{BD}}}{T}=0.00071\,\!</math> to <math>\widehat{r}(T)=0.00053.\,\!</math> The average time between failures is estimated to increase from the current 1408.38 hours to 1876.93 hours.

==Confidence Bounds==
For fleet data analysis using the Crow-AMSAA model, the confidence bounds are calculated using the same procedure described for the Crow-AMSAA (NHPP) model (See [[Crow-AMSAA Confidence Bounds]]). For fleet data analysis using the Crow Extended model, the confidence bounds are calculated using the same procedure described for the Crow Extended model (See [[Crow Extended Confidence Bounds]]).

=More Examples=
==Predicting the Number of Failures for Fleet Operation==
{{:Crow_Extended_Model_Fleet_Analysis_Example}}

Fleet Analysis Example

2014-06-12T15:33:40Z

Chris Kahn:

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Fleet_Data_Analysis|Reliability Growth and Repairable System Analysis Reference]]''.
</noinclude>

The following table presents data for a fleet of 27 systems. A cycle is a complete history from overhaul to overhaul. The failure history for the last completed cycle for each system is recorded. This is a random sample of data from the fleet. These systems are in the order in which they were selected. Suppose the intervals to group the current data are 10,000; 20,000; 30,000; 40,000 and the final interval is defined by the termination time. Conduct the fleet analysis.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="4" style="text-align:center"|'''Sample Fleet Data'''
|-
!System
!Cycle Time <math>{{T}_{j}}\,\!</math>
!Number of failures <math>{{N}_{j}}\,\!</math>
!Failure Time <math>{{X}_{ij}}\,\!</math>
|-
|1|| 1396|| 1|| 1396
|-
|2|| 4497|| 1|| 4497
|-
|3|| 525|| 1|| 525
|-
|4|| 1232|| 1|| 1232
|-
|5|| 227|| 1|| 227
|-
|6|| 135|| 1|| 135
|-
|7|| 19|| 1|| 19
|-
|8|| 812|| 1|| 812
|-
|9|| 2024|| 1|| 2024
|-
|10|| 943|| 2|| 316, 943
|-
|11|| 60|| 1|| 60
|-
|12|| 4234|| 2|| 4233, 4234
|-
|13|| 2527|| 2|| 1877, 2527
|-
|14|| 2105|| 2|| 2074, 2105
|-
|15|| 5079|| 1|| 5079
|-
|16|| 577|| 2|| 546, 577
|-
|17|| 4085|| 2|| 453, 4085
|-
|18|| 1023|| 1|| 1023
|-
|19|| 161|| 1|| 161
|-
|20|| 4767|| 2|| 36, 4767
|-
|21|| 6228|| 3|| 3795, 4375, 6228
|-
|22|| 68|| 1|| 68
|-
|23|| 1830|| 1|| 1830
|-
|24|| 1241|| 1|| 1241
|-
|25|| 2573|| 2|| 871, 2573
|-
|26|| 3556|| 1|| 3556
|-
|27|| 186|| 1|| 186
|-
|Total||52110|| 37||
|}

'''Solution'''

The sample fleet data set can be grouped into 10,000; 20,000; 30,000; 40,000 and 52,110 time intervals. The following table gives the grouped data.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Grouped Data'''
|-
!Time
!Observed Failures
|-
|10,000|| 8
|-
|20,000|| 16
|-
|30,000|| 22
|-
|40,000|| 27
|-
|52,110|| 37
|}

Based on the above time intervals, the maximum likelihood estimates of <math>\widehat{\lambda }\,\!</math> and <math>\widehat{\beta }\,\!</math> for this data set are then given by:

:<math>\begin{matrix}
\widehat{\lambda }=0.00147 \\
\widehat{\beta }=0.93328 \\
\end{matrix}\,\!</math>

The next figure shows the System Operation plot.

[[Image:rga13.7.png|center|450px]]