Arrhenius Example - Revision history

Lisa Hacker at 19:02, 18 September 2023

2023-09-18T19:02:26Z

← Older revision		Revision as of 19:02, 18 September 2023
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	<noinclude>{{Banner ALTA Examples}}		<noinclude>{{Banner ALTA Examples}}
	''This example appears in the [~~[Arrhenius_Relationship#Arrhenius-Weibull\|~~Accelerated ~~Life Testing Data Analysis Reference~~]~~] book~~.''		''This example appears in the [https://help.reliasoft.com/reference/accelerated_life_testing_data_analysis Accelerated life testing reference].''

	</noinclude>		</noinclude>

Richard House at 20:43, 31 January 2014

2014-01-31T20:43:11Z

← Older revision		Revision as of 20:43, 31 January 2014
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	Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in the [[Arrhenius_Relationship#Arrhenius_Confidence_Bounds\|Arrhenius Relationship chapter]]).		Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in the [[Arrhenius_Relationship#Arrhenius_Confidence_Bounds\|Arrhenius Relationship chapter]]).

	[[Image:~~ALTA6~~.~~10.gif~~\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6_10_new.png\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]

Richard House at 22:09, 21 September 2012

2012-09-21T22:09:02Z

← Older revision		Revision as of 22:09, 21 September 2012
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	::<math>\widehat{\beta }=4.2915822</math>		::<math>\widehat{\beta }=4.2915822\,\!</math>


	::<math>\widehat{B}=1861.6186657</math>		::<math>\widehat{B}=1861.6186657\,\!</math>


	::<math>\widehat{C}=58.9848692</math>		::<math>\widehat{C}=58.9848692\,\!</math>

Kate Racaza: typo

2012-08-14T01:28:29Z

typo

← Older revision		Revision as of 01:28, 14 August 2012
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	<noinclude>{{Banner ALTA Examples}}		<noinclude>{{Banner ALTA Examples}}
	''This ~~article~~ appears in the [[Arrhenius_Relationship#Arrhenius-Weibull\|Accelerated Life Testing Data Analysis Reference]] book.''		''This example appears in the [[Arrhenius_Relationship#Arrhenius-Weibull\|Accelerated Life Testing Data Analysis Reference]] book.''

	</noinclude>		</noinclude>

Kate Racaza: added link to ALTA book

2012-08-14T01:20:34Z

added link to ALTA book

← Older revision		Revision as of 01:20, 14 August 2012
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	<noinclude>{{Banner ALTA Examples}}</noinclude>		<noinclude>{{Banner ALTA Examples}}
			''This article appears in the [[Arrhenius_Relationship#Arrhenius-Weibull\|Accelerated Life Testing Data Analysis Reference]] book.''

			</noinclude>
	Consider the following times-to-failure data at three different stress levels.		Consider the following times-to-failure data at three different stress levels.

Kate Racaza at 01:14, 14 August 2012

2012-08-14T01:14:22Z

← Older revision		Revision as of 01:14, 14 August 2012
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	Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius_Relationship#Arrhenius_Confidence_Bounds\|Arrhenius Relationship chapter]]).		Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in the [[Arrhenius_Relationship#Arrhenius_Confidence_Bounds\|Arrhenius Relationship chapter]]).

	[[Image:ALTA6.10.gif\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.gif\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]

Kate Racaza at 01:13, 14 August 2012

2012-08-14T01:13:36Z

← Older revision		Revision as of 01:13, 14 August 2012
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	The data set was analyzed jointly and with a complete MLE solution over the entire data set, using ReliaSoft's ALTA. The analysis yields:		The data set was analyzed jointly and with a complete MLE solution over the entire data set, using ReliaSoft's ALTA. The analysis yields:


	::<math>\widehat{\beta }=4.2915822</math>		::<math>\widehat{\beta }=4.2915822</math>
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	::<math>\widehat{C}=58.9848692</math>		::<math>\widehat{C}=58.9848692</math>

	Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius Relationship~~#Appendix 6.A: Arrhenius Confidence Bounds\|Appendix 6.A~~]]).
			Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius_Relationship#Arrhenius_Confidence_Bounds\|Arrhenius Relationship chapter]]).

	[[Image:ALTA6.10.gif\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.gif\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]

Richard House at 07:23, 6 August 2012

2012-08-06T07:23:51Z

← Older revision		Revision as of 07:23, 6 August 2012
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	Consider the following times-to-failure data at three different stress levels.		Consider the following times-to-failure data at three different stress levels.

	~~<br>~~
	~~<br>~~
	[[Image:6stresstimefailed.gif\|center\|400px\|]]		[[Image:6stresstimefailed.gif\|center\|400px\|]]
	~~<br>~~

	~~<br>~~
	The data set was analyzed jointly and with a complete MLE solution over the entire data set, using ReliaSoft's ALTA. The analysis yields:		The data set was analyzed jointly and with a complete MLE solution over the entire data set, using ReliaSoft's ALTA. The analysis yields:

	~~<br>~~
	::<math>\widehat{\beta }=4.2915822</math>		::<math>\widehat{\beta }=4.2915822</math>


	~~<br>~~
	::<math>\widehat{B}=1861.6186657</math>		::<math>\widehat{B}=1861.6186657</math>


	~~<br>~~
	::<math>\widehat{C}=58.9848692</math>		::<math>\widehat{C}=58.9848692</math>

			Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius Relationship#Appendix 6.A: Arrhenius Confidence Bounds\|Appendix 6.A]]).

	~~<br>~~
	Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius Relationship#Appendix 6.A: Arrhenius Confidence Bounds\|Appendix 6.A]]).
	~~<br>~~
	[[Image:ALTA6.10.gif\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.gif\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]

Kate Racaza at 01:46, 2 August 2012

2012-08-02T01:46:44Z

← Older revision		Revision as of 01:46, 2 August 2012
Line 25:		Line 25:
	Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius Relationship#Appendix 6.A: Arrhenius Confidence Bounds\|Appendix 6.A]]).		Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius Relationship#Appendix 6.A: Arrhenius Confidence Bounds\|Appendix 6.A]]).
	<br>		<br>
	[[Image:ALTA6.10.gif\|center\|~~450px~~\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.gif\|center\|800px\|Comparison of the confidence bounds for different use stress levels.]]

Kate Racaza: increased image size

2012-08-02T01:46:03Z

increased image size

← Older revision		Revision as of 01:46, 2 August 2012
Line 25:		Line 25:
	Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius Relationship#Appendix 6.A: Arrhenius Confidence Bounds\|Appendix 6.A]]).		Once the parameters of the model are estimated, extrapolation and other life measures can be directly obtained using the appropriate equations. Using the MLE method, confidence bounds for all estimates can be obtained. Note that in the next figure, the more distant the accelerated stress is from the operating stress, the greater the uncertainty of the extrapolation. The degree of uncertainty is reflected in the confidence bounds. (General theory and calculations for confidence intervals are presented in [[Appendix A: Brief Statistical Background\|Appendix A]]. Specific calculations for confidence bounds on the Arrhenius model are presented in [[Arrhenius Relationship#Appendix 6.A: Arrhenius Confidence Bounds\|Appendix 6.A]]).
	<br>		<br>
	[[Image:ALTA6.10.gif~~\|thumb~~\|center\|~~400px~~\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.gif\|center\|450px\|Comparison of the confidence bounds for different use stress levels.]]