Three Level Compromise Test Plan for One Stress - Revision history

Kate Racaza at 18:24, 28 September 2015

2015-09-28T18:24:04Z

← Older revision		Revision as of 18:24, 28 September 2015
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	This example ~~compares~~ the results for the 3 level best compromise test plan with one stress.		This example validates the results for the 3 level best compromise test plan with one stress in ALTA.

Kate Racaza at 16:36, 13 June 2014

2014-06-13T16:36:22Z

← Older revision		Revision as of 16:36, 13 June 2014
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	{{Reference Example\|~~ALTA_Reference_Examples_Banner.png\|ALTA_Reference_Examples~~}}		{{Reference Example\|{{Banner ALTA Reference Examples}}}}

	This example compares the results for the 3 level best compromise test plan with one stress.		This example compares the results for the 3 level best compromise test plan with one stress.

Kate Racaza at 15:22, 13 June 2014

2014-06-13T15:22:46Z

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	{{Reference Example\|ALTA_Reference_Examples_Banner.png\|ALTA_Reference_Examples}}		{{Reference Example\|ALTA_Reference_Examples_Banner.png\|ALTA_Reference_Examples}}

	This example compares the results for the 3~~-Level Best Compromise~~ test plan with one stress.		This example compares the results for the 3 level best compromise test plan with one stress.


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	A Weibull distribution with an Arrhenius life stress relationship is used. The Arrhenius relationship uses the following formula:		A Weibull distribution with an Arrhenius life-stress relationship is used. The Arrhenius relationship uses the following formula:

	::<math>ln(\eta) = \beta_{0} + \beta_{1} \times \frac{11605}{T}\,\!</math>		::<math>ln(\eta) = \beta_{0} + \beta_{1} \times \frac{11605}{T}\,\!</math>
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	The ~~three-~~level compromise test plan is:		The 3 level compromise test plan is:

	* 156 units should be tested at 78°C (351.15°K)		* 156 units should be tested at 78°C (351.15°K)
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	The resulting ~~three-level best compromise~~ test plan ~~in ALTA~~ is shown below.		The resulting test plan is shown below.

Kate Racaza at 16:13, 12 June 2014

2014-06-12T16:13:26Z

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	The three level compromise test plan is:		The three-level compromise test plan is:

	* 156 units should be tested at 78°C (351.15°K)		* 156 units should be tested at 78°C (351.15°K)
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	The resulting three level best compromise test plan in ALTA is shown below.		The resulting three-level best compromise test plan in ALTA is shown below.


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	The test plan shows that:		The test plan shows that (starting at row 24 in the picture above):

	* The low stress level ~~(row 29)~~ should be 364.~~56 °K~~ (91.41°C) and about 159 units should be tested at this temperature.		* The low stress level should be 364.56°K (91.41°C) and about 159 units should be tested at this temperature.
	* The middle stress level ~~(row 30)~~ should be 378.32 °K (105.17°C) and about 60 units should be tested at this temperature.		* The middle stress level should be 378.32 °K (105.17°C) and about 60 units should be tested at this temperature.
	* The high stress level ~~(row 31)~~ should be 393.15 °K (120°C) and about 81 units should be tested at this temperature.		* The high stress level should be 393.15 °K (120°C) and about 81 units should be tested at this temperature.


	The estimated standard deviation of the log B10 life at 50°C can be obtained by:		The estimated standard deviation of the log B10 life at 50°C can be obtained by:

	::<math>Ase\left[log \left(\hat{t}_{0.1}(50) \right) \right] = \frac{Ase\hat{t}_{0.1}(50)}{\hat{t}_{0.1}(50)} = \frac{1181.94}{2990.09} = 0.3953\,\!</math>		::<math>Ase\left[log \left(\hat{t}_{0.1}(50) \right) \right] = \frac{Ase\left(\hat{t}_{0.1}(50)\right)}{\hat{t}_{0.1}(50)} = \frac{1181.94}{2990.09} = 0.3953\,\!</math>


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	'''Using ~~ALTA~~ SimuMatic to Evaluate the Test Plan'''		'''Using SimuMatic to Evaluate the Test Plan'''

	We will use the SimuMatic utility to evaluate the test plan. The following picture shows the settings used in the Main tab of SimuMatic (with <math>\alpha_{1} = \beta_{1} \times 11605\,\!</math>):		We will use the ALTA SimuMatic utility to evaluate the test plan. The following picture shows the settings used in the Main tab of SimuMatic (with <math>\alpha_{1} = \beta_{1} \times 11605\,\!</math>):

	[[Image: Compromise plan simumatic.png\|center\|600px]]		[[Image: Compromise plan simumatic.png\|center\|600px]]


	The rest of the SimuMatic ~~settings~~ are as follows:		The rest of the settings in SimuMatic are as follows:

	* Stress tab:		* Stress tab:
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	* Settings tab		* Settings tab
	::Seed = '''10''', Precision = '''4''', Number of data sets = '''1000'''		::Seed = '''10''', Precision = '''4''', Number of data sets = '''1000'''
	* Reliabilities and Times		* Reliabilities and Times tab
	::Reliability value = '''0.9'''		::Reliability value = '''0.9'''

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	We take the ~~nature~~ log of the B10 life (the last column) and calculate its standard deviation. The calculated standard deviation is 0.4062. This is very close to the analytical solution from the ALTA test plan tool, where the standard deviation is 0.3953.		We take the natural log of the B10 life (the last column) and calculate its standard deviation. The calculated standard deviation is 0.4062. This is very close to the analytical solution from the ALTA test plan tool, where the standard deviation is 0.3953.

	This standard deviation is smaller than the standard deviation given by the test plan in the book. Therefore, the test plan generated in ALTA is better than the test plan given in the book in terms of minimizing the estimation variance of the B10 life.		This standard deviation is smaller than the standard deviation given by the test plan in the book. Therefore, the test plan generated in ALTA is better than the test plan given in the book in terms of minimizing the estimation variance of the B10 life.

Kate Racaza at 16:06, 12 June 2014

2014-06-12T16:06:15Z

Kate Racaza at 17:55, 11 June 2014

2014-06-11T17:55:50Z

← Older revision		Revision as of 17:55, 11 June 2014
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	This example compares the results for the 3-Level Best Compromise test plan with one stress.		This example compares the results for the 3-Level Best Compromise test plan with one stress.


	{{Reference_Example_Heading1}}		{{Reference_Example_Heading1}}

Kate Racaza at 17:55, 11 June 2014

2014-06-11T17:55:35Z

← Older revision		Revision as of 17:55, 11 June 2014
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	{{Reference Example\|ALTA_Reference_Examples_Banner.png\|ALTA_Reference_Examples}}		{{Reference Example\|ALTA_Reference_Examples_Banner.png\|ALTA_Reference_Examples}}

	This example compares the ~~statistically optimum~~ test plan ~~result for~~ one stress ~~from the ALTA Test Plan tool~~.		This example compares the results for the 3-Level Best Compromise test plan with one stress.

	{{Reference_Example_Heading1}}		{{Reference_Example_Heading1}}

Kate Racaza at 17:46, 11 June 2014

2014-06-11T17:46:45Z

← Older revision		Revision as of 17:46, 11 June 2014
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	'''Using ALTA SimuMatic to Evaluate the Test Plan'''		'''Using ALTA SimuMatic to Evaluate the Test Plan'''

	We will use the SimuMatic utility to evaluate the test plan. The following picture shows the settings used the Main tab of SimuMatic (with <math>\alpha_{1} = \beta_{1} \times 11605\,\!</math>):		We will use the SimuMatic utility to evaluate the test plan. The following picture shows the settings used in the Main tab of SimuMatic (with <math>\alpha_{1} = \beta_{1} \times 11605\,\!</math>):

	[[Image: Compromise plan simumatic.png\|center\|600px]]		[[Image: Compromise plan simumatic.png\|center\|600px]]

Kate Racaza at 17:46, 11 June 2014

2014-06-11T17:46:03Z

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 * 84 units will be tested at temperature of 120°C (393.15°K)
-The estimated standard error for the B10 life at 50°C from this test plan is <math>Ase\left [log \left(\hat{t}_{0.1}(50) \right) \right]\,\!</math> .
+The estimated standard error for the B10 life at 50°C from this test plan is <math>Ase\left [log \left(\hat{t}_{0.1}(50) \right) \right] = 0.4375\,\!</math> .
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Kate Racaza: Created page with '{{Reference Example|ALTA_Reference_Examples_Banner.png|ALTA_Reference_Examples}} This example compares the statistically optimum test plan result for one stress from the ALTA Te…'

2014-06-11T16:49:09Z

Created page with '{{Reference Example|ALTA_Reference_Examples_Banner.png|ALTA_Reference_Examples}} This example compares the statistically optimum test plan result for one stress from the ALTA Te…'

New page

{{Reference Example|ALTA_Reference_Examples_Banner.png|ALTA_Reference_Examples}}

This example compares the statistically optimum test plan result for one stress from the ALTA Test Plan tool.

{{Reference_Example_Heading1}}

The data set is from Example 20.5 on page 542 in the book '''Statistical Methods for Reliability Data''' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.

{{Reference_Example_Heading2}}

A Weibull distribution with Arrhenius relationship is used. The Arrhenius relationship uses the following formula:

::<math>ln(\eta) = \beta_{0} + \beta_{1} \times \frac{11605}{T}\,\!</math>

The planning values of the model parameters used in the test plan are <math>\beta\,\!</math> = 1.667,   <math>\beta_{0}\,\!</math> = -16.7333 and <math>\beta_{1}\,\!</math> = 0.7265. These planning values were obtained based on the following assumptions: 0.1% of the units will fail in 6 months (183 hours) at 50°C, and 90% would fail in 6 months at 120°C. This information is given in Example 20.2 on page 535.

The use temperature is 50°C (323.15°K) and the highest temperature used in the test is 120°C (393.15 °K).

A total of 300 units are available for testing. Three temperature levels can be used and 20% of the units will be tested at the middle temperature level. The objective of the test plan is to:

* Determine the three temperature levels used in the test.
* Determine the number of test units at the high and the low temperature level.

Tests will be conducted using the created test plan. The failure data from the test is then used to estimate the model parameters and the reliability model is used to predict the B10 life at 50°C and its variance.

We need to find a test plan with three temperature levels that will minimize the estimation variance for the B10 life at 50°C.

{{Reference_Example_Heading3}}

The three level compromise test plan is:

* 156 units will be tested at temperature of 78°C (351.15°K)
* 60 units will be tested at temperature of 98°C (371.15°K)
* 84 units will be tested at temperature of 120°C (393.15°K)

The estimated standard error for the B10 life at 50°C from this test plan is <math>Ase\left [log \left(\hat{t}_{0.1}(50) \right) \right]\,\!</math> .

{{Reference_Example_Heading4|ALTA}}

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	The data set is from Example 20.5 on page 542 in the book '''Statistical Methods for Reliability Data''' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.		The data set is from Example 20.5 on page 542 in the book ''Statistical Methods for Reliability Data'' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.


	{{Reference_Example_Heading2}}		{{Reference_Example_Heading2}}

	A Weibull distribution with Arrhenius relationship is used. The Arrhenius relationship uses the following formula:		A Weibull distribution with an Arrhenius life stress relationship is used. The Arrhenius relationship uses the following formula:

	::<math>ln(\eta) = \beta_{0} + \beta_{1} \times \frac{11605}{T}\,\!</math>		::<math>ln(\eta) = \beta_{0} + \beta_{1} \times \frac{11605}{T}\,\!</math>


	The planning values of the model parameters ~~used in~~ the test plan are <math>\beta\,\!</math> = 1.667,   <math>\beta_{0}\,\!</math> = -16.7333 and <math>\beta_{1}\,\!</math> = 0.7265. These planning values were obtained based on the following assumptions: 0.1% of the units will fail in 6 months (183 hours) at 50°C, and 90% ~~would~~ fail in 6 months at 120°C. This information is given in Example 20.2 on page 535.		The planning values of the model parameters for the test plan are <math>\beta\,\!</math> = 1.667,   <math>\beta_{0}\,\!</math> = -16.7333 and <math>\beta_{1}\,\!</math> = 0.7265. These planning values were obtained based on the following assumptions: 0.1% of the units will fail in 6 months (183 hours) at 50°C, and 90% will fail in 6 months at 120°C. This information is given in Example 20.2 on page 535.

	The use temperature is 50°C (323.15°K) and the highest temperature used in the test is 120°C (393.15 °K).		The use temperature is 50°C (323.15°K) and the highest temperature that can be used in the test is 120°C (393.15 °K).

	A total of 300 units are available for testing. Three temperature levels can be used and 20% of the units will be tested at the middle temperature level. The ~~objective~~ of the test plan is to:		A total of 300 units are available for testing. Three temperature levels can be used and 20% of the units will be tested at the middle temperature level. The objectives of the test plan are to:

	* Determine the three temperature levels used in the test.		* Determine the three temperature levels that should be used in the test.
	* Determine the number of test units at the high and the low temperature ~~level~~.		* Determine the number of test units at the high and the low temperature levels.

	Tests will be conducted using the created test plan. The failure data from the test ~~is then~~ used to estimate the model parameters and the reliability model is used to predict the B10 life at 50°C and its variance.		Tests will be conducted using the created test plan. The failure data from the test will be used to estimate the model parameters and the reliability model, which are then used to predict the B10 life at 50°C and its variance. Therefore, we need a test plan that will minimize the estimation variance for the B10 life at 50°C.

	We need ~~to find~~ a test plan ~~with three temperature levels~~ that will minimize the estimation variance for the B10 life at 50°C.


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	The three level compromise test plan is:		The three level compromise test plan is:

	* 156 units ~~will~~ be tested at ~~temperature of~~ 78°C (351.15°K)		* 156 units should be tested at 78°C (351.15°K)
	* 60 units ~~will~~ be tested at ~~temperature of~~ 98°C (371.15°K)		* 60 units should be tested at 98°C (371.15°K)
	* 84 units ~~will~~ be tested at ~~temperature of~~ 120°C (393.15°K)		* 84 units should be tested at 120°C (393.15°K)

	~~The~~ estimated standard error for the B10 life at 50°C ~~from this test plan~~ is <math>Ase\left [log \left(\hat{t}_{0.1}(50) \right) \right] = 0.4375\,\!</math> .		Based on this test plan, the estimated standard error for the B10 life at 50°C is <math>Ase\left [log \left(\hat{t}_{0.1}(50) \right) \right] = 0.4375\,\!</math> .