Temperature-Nonthermal (TNT)-Weibull Model - Revision history

Kate Racaza at 18:21, 28 September 2015

2015-09-28T18:21:02Z

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	{{Reference Example\|{{Banner ALTA Reference Examples}}}}		{{Reference Example\|{{Banner ALTA Reference Examples}}}}

	This example ~~compares~~ the ~~results~~ for the temperature-nonthermal life-stress relationship with a Weibull distribution.		This example validates the calculations for the temperature-nonthermal life-stress relationship with a Weibull distribution in ALTA standard folios.

Kate Racaza at 23:08, 16 June 2014

2014-06-16T23:08:26Z

← Older revision		Revision as of 23:08, 16 June 2014
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	{{Reference_Example_Heading4\|ALTA}}		{{Reference_Example_Heading4\|ALTA}}

	We will first perform the analysis using the general log-linear (GLL) life-stress relationship, and then compare its results with the temperature-nonthermal ~~model~~ (TNT) life-stress relationship.		We will first perform the analysis using the general log-linear (GLL) life-stress relationship, and then compare its results with the temperature-nonthermal (TNT) life-stress relationship.


	'''General Log-Linear (GLL)-Weibull Model'''		'''General Log-Linear (GLL)-Weibull Model'''

	To use the GLL-Weibull model with the same life-stress relationship as the one in the book, the following stress ~~transformation~~ should be used:		To use the GLL-Weibull model with the same life-stress relationship as the one in the book, the following stress transformations should be used:

	[[image:Two Stress GLL Weibull_Stress Transform.png\|center]]		[[image:Two Stress GLL Weibull_Stress Transform.png\|center]]

Beth Ann Paape at 21:27, 16 June 2014

2014-06-16T21:27:06Z

← Older revision		Revision as of 21:27, 16 June 2014
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	'''General Log-Linear (GLL)-Weibull Model'''		'''General Log-Linear (GLL)-Weibull Model'''

	To use the GLL-Weibull model ~~have~~ the same life-stress relationship as the one in the book, the following stress transformation should be used:		To use the GLL-Weibull model with the same life-stress relationship as the one in the book, the following stress transformation should be used:

	[[image:Two Stress GLL Weibull_Stress Transform.png\|center]]		[[image:Two Stress GLL Weibull_Stress Transform.png\|center]]

Beth Ann Paape at 18:15, 16 June 2014

2014-06-16T18:15:48Z

Beth Ann Paape at 18:11, 16 June 2014

2014-06-16T18:11:02Z

← Older revision		Revision as of 18:11, 16 June 2014
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	We will first perform the analysis using the general log-linear (GLL) life-stress relationship, and then compare its results with the temperature-nonthermal model (TNT) life-stress relationship.		We will first perform the analysis using the general log-linear (GLL) life-stress relationship, and then compare its results with the temperature-nonthermal model (TNT) life-stress relationship.

			'''General Log-Linear (GLL)-Weibull Model'''

			To use the GLL-Weibull model have the same life-stress relationship as the one in the book, the following stress transformation should be used:

	[[image:Two Stress GLL Weibull_Stress Transform.png\|center]]		[[image:Two Stress GLL Weibull_Stress Transform.png\|center]]
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	Temperature-Nonthermal (TNT)-Weibull Model		'''Temperature-Nonthermal (TNT)-Weibull Model'''

	If we use the temperature-nonthermal life-stress relationship to analyze the data, the same results would be obtained, as shown in the following picture. Therefore, by selecting the appropriate stress transformations, a general log-linear model can become a temperature-nonthermal model.		If we use the temperature-nonthermal life-stress relationship to analyze the data, the same results would be obtained, as shown in the following picture. Therefore, by selecting the appropriate stress transformations, a general log-linear model can become a temperature-nonthermal model.

	[[image:Two Stress GLL Weibull_Analysis Summary TNT.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary TNT.png\|center]]

Beth Ann Paape at 18:09, 16 June 2014

2014-06-16T18:09:02Z

← Older revision		Revision as of 18:09, 16 June 2014
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	*The maximum likelihood estimation (MLE) results for the parameters are: <math>\,\!\alpha _{0}=0.671</math> , <math>\,\!\alpha _{1}=4640.1</math> , <math>\,\!\alpha _{2}=-0.445</math> and <math>\,\!\beta =1.805</math>.		*The maximum likelihood estimation (MLE) results for the parameters are: <math>\,\!\alpha _{0}=0.671</math> , <math>\,\!\alpha _{1}=4640.1</math> , <math>\,\!\alpha _{2}=-0.445</math> and <math>\,\!\beta =1.805</math>.

	*The eta parameter in the Weibull distribution at temperature of 30°C (303.15 K) and switching rate of 5 cycles/minute is estimated as <math>\,\!4.244\times 10^{6}</math>.		*The <math>\,\!\eta</math> parameter in the Weibull distribution at temperature of 30°C (303.15 K) and switching rate of 5 cycles/minute is estimated as <math>\,\!4.244\times 10^{6}</math>.

	*The estimated reliability at 200,000 cycles and temperature of 30°C (303.15 K) and switching rate of 5 cycles/minute is 0.996. Its one-sided lower 90% confidence bound is 0.992.		*The estimated reliability at 200,000 cycles and temperature of 30°C (303.15 K) and switching rate of 5 cycles/minute is 0.996. Its one-sided lower 90% confidence bound is 0.992.

Beth Ann Paape at 18:08, 16 June 2014

2014-06-16T18:08:14Z

← Older revision		Revision as of 18:08, 16 June 2014
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	[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''~~Result~~ in ALTA'''</div>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Results in ALTA'''</div>

Beth Ann Paape at 18:06, 16 June 2014

2014-06-16T18:06:41Z

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	[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Result in ALTA</div>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Result in ALTA'''</div>


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	[[image:Two Stress GLL Weibull_Analysis Summary GLL new alpha.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary GLL new alpha.png\|center]]
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Altered Parameters</div>~~Altered Parameters~~		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Altered Parameters'''</div>


	:This likelihood value is slightly smaller than the value that was originally calculated in ALTA, which was -710.268519. Therefore, the result in ALTA is better in terms of maximizing the log likelihood value.		:This likelihood value is slightly smaller than the value that was originally calculated in ALTA, which was -710.268519. Therefore, the result in ALTA is better in terms of maximizing the log likelihood value.

Beth Ann Paape at 18:03, 16 June 2014

2014-06-16T18:03:04Z

← Older revision		Revision as of 18:03, 16 June 2014
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	[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Result in ALTA</div>~~Result in ALTA~~		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Result in ALTA</div>


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	[[image:Two Stress GLL Weibull_Analysis Summary GLL new alpha.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary GLL new alpha.png\|center]]
	Altered Parameters		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Altered Parameters</div>Altered Parameters

	:This likelihood value is slightly smaller than the value that was originally calculated in ALTA, which was -710.268519. Therefore, the result in ALTA is better in terms of maximizing the log likelihood value.		:This likelihood value is slightly smaller than the value that was originally calculated in ALTA, which was -710.268519. Therefore, the result in ALTA is better in terms of maximizing the log likelihood value.

Beth Ann Paape at 18:01, 16 June 2014

2014-06-16T18:01:36Z

← Older revision		Revision as of 18:01, 16 June 2014
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	[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]
	Result in ALTA		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Result in ALTA</div>Result in ALTA

← Older revision		Revision as of 18:15, 16 June 2014
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	We will first perform the analysis using the general log-linear (GLL) life-stress relationship, and then compare its results with the temperature-nonthermal model (TNT) life-stress relationship.		We will first perform the analysis using the general log-linear (GLL) life-stress relationship, and then compare its results with the temperature-nonthermal model (TNT) life-stress relationship.


	'''General Log-Linear (GLL)-Weibull Model'''		'''General Log-Linear (GLL)-Weibull Model'''
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	*Based on this model, the maximum likelihood estimation (MLE) results for the parameters are:		Based on this model, the maximum likelihood estimation (MLE) results for the parameters are:

	[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary GLL.png\|center]]
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	:These results are slightly different from the results given in the book (especially for <math>\,\!\alpha _{2}</math>). To see what the log likelihood value (LK Value) would be if we used the parameter values in the book, we use the Alter Parameters tool, as shown next.		These results are slightly different from the results given in the book (especially for <math>\,\!\alpha _{2}</math>). To see what the log likelihood value (LK Value) would be if we used the parameter values in the book, we use the Alter Parameters tool, as shown next.

	[[image:Two Stress GLL Weibull_Alter Parameters.png\|center]]		[[image:Two Stress GLL Weibull_Alter Parameters.png\|center]]


	:The resulting LK Value for the altered parameters is -710.356064, as shown next.		The resulting LK Value for the altered parameters is -710.356064, as shown next.

	[[image:Two Stress GLL Weibull_Analysis Summary GLL new alpha.png\|center]]		[[image:Two Stress GLL Weibull_Analysis Summary GLL new alpha.png\|center]]
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	:This likelihood value is slightly smaller than the value that was originally calculated in ALTA, which was -710.268519. Therefore, the result in ALTA is better in terms of maximizing the log likelihood value.		This likelihood value is slightly smaller than the value that was originally calculated in ALTA, which was -710.268519. Therefore, the result in ALTA is better in terms of maximizing the log likelihood value.

	Using the parameters originally calculated in ALTA:		Using the parameters originally calculated in ALTA:

	*The <math>\,\!\eta</math> parameter in the Weibull distribution at temperature of 30°C (303.15 K) and switching rate of 5 cycles/minute is estimated as <math>\,\!4.172\times 10^{6}</math> .		*The <math>\,\!\eta</math> parameter in the Weibull distribution at temperature of 30°C (303.15 K) and switching rate of 5 cycles/minute is estimated as <math>\,\!4.172\times 10^{6}</math>.

	*The estimated reliability at 200,000 cycles and temperature of 30°C (303.15 F) and switching rate of 5 cycles/minute is 0.996. Its one-sided lower 90% confidence bound is 0.992, as shown next.		*The estimated reliability at 200,000 cycles and temperature of 30°C (303.15 F) and switching rate of 5 cycles/minute is 0.996. Its one-sided lower 90% confidence bound is 0.992, as shown next.