ALTA ALTA Standard Folio Data PPH-Weibull - Revision history

Richard House: Redirected page to Template:WebNotes/ALTAALTA Standard Folio Data PHazards

2015-07-08T19:55:41Z

Redirected page to Template:WebNotes/ALTAALTA Standard Folio Data PHazards

← Older revision		Revision as of 19:55, 8 July 2015
Line 1:		Line 1:
	~~{{Template:NoSkin}}~~		#REDIRECT [[Template:WebNotes/ALTAALTA_Standard_Folio_Data_PHazards]]
	~~{\| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;"~~
	\|-
	~~\| valign="middle" align="left" bgcolor=EEEEEE\|~~[[~~Image: Webnotes-alta.png \|center\|195px]]~~
	\|}
	~~{\| class="FCK__ShowTableBorders" border="0" cellspacing="1" cellpadding="1"~~
	\|-
	~~\| valign="middle" \|{{Font\|Standard Folio Proportional Hazards-Weibull\|11\|tahoma\|bold\|gray}}~~
	\|-
	~~\| valign="middle" \|~~
	Introduced by D. R. Cox, the Proportional Hazards (PH) model was developed in order to estimate the effects of different covariates influencing the times-to-failure of a system. The model has been widely used in the biomedical field, and recently there has been an increasing interest in its application in reliability engineering. In its original form, the model is non-parametric, i.e. no assumptions are made about the nature or shape of the underlying failure distribution. In ALTA, the proportional hazards model is included in its parametric form and can be used to analyze data with up to eight variables.

	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~
	~~<br>~~

	~~[[File~~:~~docedit.png\|20px\|right\|link=http://www.reliawiki.com~~/~~index.php?title=ALTA_ALTA_Standard_Folio_Data_PPH-Weibull&action=edit~~]]

Lisa Hacker at 03:53, 26 July 2012

2012-07-26T03:53:33Z

@@ Line 10: / Line 10: @@
 | valign="middle" |
 Introduced by D. R. Cox, the Proportional Hazards (PH) model was developed in order to estimate the effects of different covariates influencing the times-to-failure of a system. The model has been widely used in the biomedical field, and recently there has been an increasing interest in its application in reliability engineering. In its original form, the model is non-parametric, i.e. no assumptions are made about the nature or shape of the underlying failure distribution.  In ALTA, the proportional hazards model is included in its parametric form and can be used to analyze data with up to eight variables.
 <br>
 <br>

Athanasios Gerokostopoulos at 18:38, 16 April 2012

2012-04-16T18:38:16Z

← Older revision		Revision as of 18:38, 16 April 2012
Line 6:		Line 6:
	{\| class="FCK__ShowTableBorders" border="0" cellspacing="1" cellpadding="1"		{\| class="FCK__ShowTableBorders" border="0" cellspacing="1" cellpadding="1"
	\|-		\|-
	\| valign="middle" \|{{Font\|Standard Folio ~~Data PPH~~-Weibull\|11\|tahoma\|bold\|gray}}		\| valign="middle" \|{{Font\|Standard Folio Proportional Hazards-Weibull\|11\|tahoma\|bold\|gray}}
	\|-		\|-
	\| valign="middle" \|		\| valign="middle" \|
	~~The ALTA standard folio is used to perform quantitative accelerated life testing data analysis~~. ~~In this analysis~~, the ~~engineer extrapolates a product’s failure behavior at normal conditions from life data obtained at accelerated stress levels. Since products fail more quickly at accelerated stress levels, this sort~~ of ~~analysis allows~~ the ~~engineer~~ to ~~obtain reliability information about~~ a ~~product (e~~.g., ~~mean life~~, ~~probability~~ of failure ~~at a specific time~~, ~~etc.)~~ in ~~a shorter time~~.		Introduced by D. R. Cox, the Proportional Hazards (PH) model was developed in order to estimate the effects of different covariates influencing the times-to-failure of a system. The model has been widely used in the biomedical field, and recently there has been an increasing interest in its application in reliability engineering. In its original form, the model is non-parametric, i.e. no assumptions are made about the nature or shape of the underlying failure distribution. In ALTA, the proportional hazards model is included in its parametric form and can be used to analyze data with up to eight variables.
	\|}		\|}
	<br>		<br>

Nikki Helms at 20:57, 22 March 2012

2012-03-22T20:57:44Z

← Older revision		Revision as of 20:57, 22 March 2012
Line 19:		Line 19:
	\|-		\|-
	\| [[Image:Book blue.png]]		\| [[Image:Book blue.png]]
	\| [http://reliawiki.~~com~~/index.php/~~Template~~:~~PH_Model~~ the theory textbook...]		\| [http://reliawiki.org/index.php/Multivariable_Relationships:_General_Log-Linear_and_Proportional_Hazards the theory textbook...]
	\|-		\|-
	\| [[Image:Articleblue.png]]		\| [[Image:Articleblue.png]]

Nikki Helms at 22:44, 21 March 2012

2012-03-21T22:44:20Z

← Older revision		Revision as of 22:44, 21 March 2012
Line 52:		Line 52:

	[[File:docedit.png\|20px\|right\|link=http://www.reliawiki.com/index.php?title=ALTA_ALTA_Standard_Folio_Data_PPH-Weibull&action=edit]]		[[File:docedit.png\|20px\|right\|link=http://www.reliawiki.com/index.php?title=ALTA_ALTA_Standard_Folio_Data_PPH-Weibull&action=edit]]

	~~[[Category:Needs example]]~~

Nikki Helms at 22:42, 21 March 2012

2012-03-21T22:42:13Z

← Older revision		Revision as of 22:42, 21 March 2012
Line 25:		Line 25:
	\|-		\|-
	\| [[Image:Bulbblue.png]]		\| [[Image:Bulbblue.png]]
	\| [http://~~www.~~reliawiki.com/index.php/~~Temporary_needs_example_page~~ use example(s)...]		\| [http://reliawiki.com/index.php/Proportional_Hazards_Medical_Data_Example use example(s)...]
	\|}		\|}

Nikki Helms at 20:55, 21 March 2012

2012-03-21T20:55:18Z

← Older revision		Revision as of 20:55, 21 March 2012
Line 9:		Line 9:
	\|-		\|-
	\| valign="middle" \|		\| valign="middle" \|
	~~Content 1~~		The ALTA standard folio is used to perform quantitative accelerated life testing data analysis. In this analysis, the engineer extrapolates a product’s failure behavior at normal conditions from life data obtained at accelerated stress levels. Since products fail more quickly at accelerated stress levels, this sort of analysis allows the engineer to obtain reliability information about a product (e.g., mean life, probability of failure at a specific time, etc.) in a shorter time.
	\|}		\|}
	<br>		<br>

Nikki Helms at 23:07, 7 March 2012

2012-03-07T23:07:14Z

← Older revision		Revision as of 23:07, 7 March 2012
Line 16:		Line 16:
	\|-		\|-
	\| [[Image:Helpblue.png]]		\| [[Image:Helpblue.png]]
	\| [~~Link1~~ the help files...]		\| [http://help.synthesis8.com/weibull_alta8/alta_standard_folios.htm the help files...]
	\|-		\|-
	\| [[Image:Book blue.png]]		\| [[Image:Book blue.png]]

Nikki Helms at 22:44, 7 March 2012

2012-03-07T22:44:34Z

← Older revision		Revision as of 22:44, 7 March 2012
Line 9:		Line 9:
	\|-		\|-
	\| valign="middle" \|		\| valign="middle" \|
	~~Solving for the parameters that maximize Eqn. (PH LKV) will yield the parameters for the PH-Weibull model. Note that for <math>\beta </math> =~~ 1~~, Eqn. (PH LKV) becomes the likelihood function for the PH-exponential model, which is similar to the original form of the proportional hazards model proposed by Cox [28].~~		Content 1
	~~<br>~~
	Note that the likelihood function given by Eqn. (GLL-LK) is very similar to the likelihood function for the proportional hazards-Weibull model given by Eqn. (PH LKV). In particular, the shape parameter of the Weibull distribution can be included in the regression coefficients of Eqn. (13) as follows:
	~~<br>~~
	~~<math>{{a}_{i,PH}}=-\beta \cdot {{a}_{i,GLL}}</math>~~
	~~<br>~~
	~~where:~~
	~~<br>~~
	~~• <math>{{a}_{i,PH}}</math> are the parameters of the PH model.~~

	~~• <math>{{a}_{i,GLL}}</math> are the parameters of the general log-linear model.~~

	In this case, the likelihood functions given by Eqns. (PH LKV) and (GLL-LK) are identical. Therefore, if no transformation on the covariates is performed, the parameter values that maximize Eqn. (GLL-LK) also maximize the likelihood function for the proportional hazards-Weibull (PHW) model with parameters given by Eqn. (GLL Parameters). Note that for <math>\beta </math> = 1 (exponential life distribution), Eqns. (PH LKV) and (GLL-LK) are identical, and <math>{{a}_{i,PH}}=-{{a}_{i,GLL}}.</math>
	~~<br>~~
	\|-
	~~\| valign="middle" \| [http://reliawiki.com/index.php/Template:PH_Model PH Model]~~
	\|}		\|}
	<br>		<br>
Line 37:		Line 22:
	\|-		\|-
	\| [[Image:Articleblue.png]]		\| [[Image:Articleblue.png]]
	\| [~~Link3~~ related article(s)...]		\| [http://www.weibull.com/hotwire/issue9/hottopics9.htm related article(s)...]
	\|-		\|-
	\| [[Image:Bulbblue.png]]		\| [[Image:Bulbblue.png]]

Nikki Helms at 22:35, 7 March 2012

2012-03-07T22:35:28Z

@@ Line 7: / Line 7: @@
 |-
 | valign="middle" |{{Font|Standard Folio Data PPH-Weibull|11|tahoma|bold|gray}}
 |-
 | valign="middle" |
@@ Line 28: / Line 26: @@
 | valign="middle" | [http://reliawiki.com/index.php/Template:PH_Model PH Model]
 |}
 <br>