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==Simulation==
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When analyzing developmental systems for reliability growth and conducting data analysis of fielded repairable systems, it is often useful to experiment with various what if scenarios or put together hypothetical analyses before having available test data in order to find the best way to analyze data when they become available. With that in mind, RGA 7 offers applications based on Monte Carlo simulation that can be used in order to:
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:a) better understand reliability growth concepts.
:b) experiment with the impact of sample size, test time and growth parameters on analysis results.
:c) construct simulation-based confidence intervals.
:d) better understand concepts behind confidence intervals.
:e) design reliability demonstration tests.
 
 
There are two applications of the Monte Carlo simulation in RGA 7. One is called Generate Monte Carlo Data and the other is called SimuMatic.
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{{generate monte carlo data}}
 
===SimuMatic===
Reliability growth analysis using simulation can be a valuable tool for reliability practitioners. With this approach, reliability growth analyses are performed a large number of times on data sets that have been created using Monte Carlo simulation.
RGA 7's SimuMatic utility generates calculated values of beta and lambda parameters, based on user specified input parameters of beta and lambda. SimuMatic essentially performs a user defined number of Monte Carlo simulations based on user defined required test time or failure termination settings, and then recalculates the beta and lambda parameters for each of the generated data sets. The number of times that the Monte Carlo data sets are generated and the parameters are re-calculated is also user defined. The final output presents the calculated values of beta and lambda and allows for various types of analysis.
To access the SimuMatic utility, either choose Project > Add Other Tools > Add SimuMatic or click the SimuMatic icon on the Project toolbar. For all of the data sets, the basic parameters that are always specified are the beta  <math>(\beta )</math>  and lambda  <math>(\lambda )</math>  parameters of the Crow-AMSAA (NHPP) model or the Power Law model.
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'''Failure Times'''
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The data set is generated assuming a single system. There is a choice between a time terminated test, where the termination time needs to be specified, or a failure terminated test, where the number of failures needs to be specified. SimuMatic will return the calculated values of  <math>\beta </math>  and  <math>\lambda </math>  for a specified number of data sets.
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'''Grouped Failure Times'''
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The data set is generated assuming a single system. There is a choice between a time terminated test, where the termination time needs to be specified, or a failure terminated test, where the number of failures needs to be specified. In addition, constant or user defined intervals need to be specified for the grouping of the data. SimuMatic will return the calculated values of  <math>\beta </math>  and  <math>\lambda </math>  for a specified number of data sets.
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'''Multiple Systems - Concurrent'''
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In this case, the number of systems needs to be specified. There is a choice between a time terminated test, where the termination time needs to be specified, or a failure terminated test, where the number of failures needs to be specified. SimuMatic will return the calculated values of  <math>\beta </math>  and  <math>\lambda </math>  for a specified number of data sets.
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'''Repairable Systems'''
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In this case, the number of systems needs to be specified. There is a choice between a time terminated test, where the termination time needs to be specified, or a failure terminated test, where the number of failures needs to be specified. SimuMatic will return the calculated values of  <math>\beta </math>  and  <math>\lambda </math>  for a specified number of data sets.
Figure simumatic input shows the Main tab of the SimuMatic window where all the necessary user inputs for a multiple systems - concurrent data set have been entered. 
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Figure simumatic output shows the generated results based on the input of Figure simumatic input. The sorted tab is shown, which allows us to extract conclusions about simulation generated confidence bounds, since the lambda and beta parameters and any other additional output are sorted by percentage. The Analysis tab allows the user to specify the confidence level for simulation generated confidence bounds as shown in Figure confidence bounds from simulation, where simulation confidence bounds are drawn for the cumulative number of failures based on the input parameters specified in Figure simumatic input. Extra results based on the calculated lambda and beta parameters can be generated in the Results tab, for example the instantaneous MTBF given a specific test time. This would be calculated as an additional result in addition to the lambda and beta parameters.
 
<math></math>
[[Image:rga14.5.png|thumb|center|300px|The SimuMatic input window.]]
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[[Image:rga14.6.png|thumb|center|300px|SimuMatic output sorted by percentile.]]
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[[Image:rga14.7.png|thumb|center|300px|Simulation generated confidence bounds on cumulative number of failures.]]
 
 
====Example 2====
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A manufacturer wants to design a reliability growth test for a redesigned product, in order to achieve an MTBF of 1,000 hours. Simulation is chosen to estimate the 1-sided 90% confidence bound on the required time to achieve the goal MTBF of 1,000 hours and the 1-sided 90% lower confidence bound on the MTBF at the end of the test time. The total test time is expected to be 15,000 hours. Based on historical data for the previous version, the expected beta and lambda parameters of the test are 0.5 and 0.3, respectively. Do the following:
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:1) Generate 1,000 data sets using SimuMatic along with the required output.
:2) Plot the instantaneous MTBF vs. time with the 90% confidence bounds.
:3) Estimate the 1-sided 90% lower confidence bound on time for an MTBF of 1,000 hours.
:4) Estimate the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test.
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=====Solution=====
:1) Figure Simumaticindow shows the SimuMatic window with all the appropriate inputs for creating the data sets.
 
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[[Image:rga14.8.png|thumb|center|300px|The Main tab of the SimuMatic window.]]
 
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Figure Simumaticnalysis and Figure Simumaticesults show the settings in the Analysis and Results tab of the SimuMatic window in order to obtain the desired outputs.
 
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[[Image:rga14.9.png|thumb|center|300px|The '''Analysis''' tab of the SimuMatic window.]]
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[[Image:rga14.10.png|thumb|center|300px|The '''Results''' tba of the SimuMatic window.]]
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Figure Simumaticata displays the results of the simulation. The columns labeled Beta and Lambda contain the different parameters obtained by calculating each data set generated via simulation for the 1,000 data sets. The IMTBF(15,000) column contains the instantaneous MTBF at 15,000 hours (the end of test time) given the parameters obtained by calculating each data set generated via simulation. The Target DMTBF column contains the time required for the MTBF to reach 1,000 hours, given the parameters obtained from the simulation.
 
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[[Image:rga14.11.png|thumb|center|300px|Simulation results using SimuMatic.]]
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[[Image:rga14.12.png|thumb|center|300px|Instantaneous MTBF with 90% confidence bounds.]]
 
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:2) Figure SimumaticMTBF shows the plot of the instantaneous MTBF with the 90% confidence bounds.
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:3) The 1-sided 90% lower confidence bound on time assuming MTBF = 1,000 hours can be obtained from the results of the simulation. On the Sorted sheet of the results, this is the target DMTBF value that corresponds to 10.00%, as shown in Figure Simumaticorted. Therefore the 1-sided 90% lower confidence bound on time is 12,642.21 hours.
 
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:4) Figure SimumaticMTBFarget shows the 1-sided 90% lower confidence bound on time in the instantaneous MTBF plot. This is indicated by the target lines on the plot.
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:5) The 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is again obtained from the Sorted sheet of the simulation results by looking at the value in the IMTBF(15,000) column that corresponds to 10.00%. As seen in Figure Simumaticorted, the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is 605.93 hours.
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[[Image:rga14.13.png|thumb|center|300px|The 1-sided 90% lower confidence bound on time assuming 1,000 hours MTBF.]]
 
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[[Image:rga14.14.png|thumb|center|300px|Instantaneous MTBF with the target.]]
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Latest revision as of 20:42, 24 June 2015

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