Template:Arrhenius-weibull example - Revision history

Kate Racaza: Redirected page to Arrhenius Example

2012-08-14T01:15:04Z

← Older revision		Revision as of 01:15, 14 August 2012
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			#REDIRECT [[Arrhenius_Example]]
	~~===Arrhenius-Weibull Example===~~

	~~Consider the following times-to-failure data at three different stress levels.~~

	~~[[Image:6stresstimefailed.png\|center\|300px\|]]~~

	~~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{B}=1861.6186657</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 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]]).~~

	[[~~Image:ALTA6.10.png\|center\|600px\|Comparison of the confidence bounds for different use stress levels.~~]]

Richard House: /* Arrhenius-Weibull Example */

2012-08-08T06:15:37Z

Arrhenius-Weibull Example

← Older revision		Revision as of 06:15, 8 August 2012
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	===Arrhenius-Weibull Example===		===Arrhenius-Weibull Example===
	~~<br>~~
	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.png\|center\|300px\|]]		[[Image:6stresstimefailed.png\|center\|300px\|]]
	~~<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 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 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.png\|center\|600px\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.png\|center\|600px\|Comparison of the confidence bounds for different use stress levels.]]

Chris Kahn: /* Arrhenius-Weibull Example */

2012-06-22T15:34:15Z

Arrhenius-Weibull Example

← Older revision		Revision as of 15:34, 22 June 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 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 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.png\|center\|~~500px~~\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.png\|center\|600px\|Comparison of the confidence bounds for different use stress levels.]]

Chris Kahn: /* Arrhenius-Weibull Example */

2012-06-22T15:32:56Z

Arrhenius-Weibull Example

← Older revision		Revision as of 15:32, 22 June 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 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 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.png\|center\|~~400px~~\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.png\|center\|500px\|Comparison of the confidence bounds for different use stress levels.]]

Chris Kahn: /* Arrhenius-Weibull Example */

2012-06-22T15:32:44Z

Arrhenius-Weibull Example

← Older revision		Revision as of 15:32, 22 June 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 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 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.png\|center\|~~250px~~\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.png\|center\|400px\|Comparison of the confidence bounds for different use stress levels.]]

Chris Kahn: /* Arrhenius-Weibull Example */

2012-06-22T15:32:26Z

Arrhenius-Weibull Example

← Older revision		Revision as of 15:32, 22 June 2012
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	<br>		<br>
	<br>		<br>
	[[Image:6stresstimefailed.png\|center\|~~175px~~\|]]		[[Image:6stresstimefailed.png\|center\|300px\|]]
	<br>		<br>

Chuck Smith: /* Arrhenius-Weibull Example */

2012-04-26T16:00:48Z

Arrhenius-Weibull Example

← Older revision		Revision as of 16:00, 26 April 2012
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	<br>		<br>
	<br>		<br>
	[[Image:6stresstimefailed.png\|center\|~~350px~~\|]]		[[Image:6stresstimefailed.png\|center\|175px\|]]
	<br>		<br>

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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 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 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.png\|center\|~~600px~~\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.png\|center\|250px\|Comparison of the confidence bounds for different use stress levels.]]

Nicolette Young: /* Arrhenius-Weibull Example */

2012-04-03T16:56:22Z

Arrhenius-Weibull Example

← Older revision		Revision as of 16:56, 3 April 2012
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	<br>		<br>
	<br>		<br>
	[[Image:6stresstimefailed.png\|center\|~~400px~~\|]]		[[Image:6stresstimefailed.png\|center\|350px\|]]
	<br>		<br>

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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 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 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.png\|center\|~~700px~~\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.png\|center\|600px\|Comparison of the confidence bounds for different use stress levels.]]

Nicolette Young: /* Arrhenius-Weibull Example */

2012-04-03T16:55:00Z

Arrhenius-Weibull Example

← Older revision		Revision as of 16:55, 3 April 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 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 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.png\|center\|~~500px~~\|Comparison of the confidence bounds for different use stress levels.]]		[[Image:ALTA6.10.png\|center\|700px\|Comparison of the confidence bounds for different use stress levels.]]

Nicolette Young: /* Arrhenius-Weibull Example */

2012-03-23T16:55:24Z

Arrhenius-Weibull Example

← Older revision		Revision as of 16:55, 23 March 2012
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	<br>		<br>
	<br>		<br>
	[[Image:6stresstimefailed.~~gif\|thumb~~\|center\|400px\|]]		[[Image:6stresstimefailed.png\|center\|400px\|]]
	<br>		<br>

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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 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 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.png\|center\|500px\|Comparison of the confidence bounds for different use stress levels.]]