Degradation Data Analysis with a Power Regression Model - Revision history

Kate Racaza at 16:22, 28 September 2015

2015-09-28T16:22:53Z

← Older revision		Revision as of 16:22, 28 September 2015
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	{{Reference Example}}		{{Reference Example}}

	This example ~~compares~~ the results for a degradation analysis with a power regression model.		This example validates the results for a degradation analysis with a power regression model in Weibull++ degradation folios.

Kate Racaza at 16:59, 9 June 2014

2014-06-09T16:59:53Z

← Older revision		Revision as of 16:59, 9 June 2014
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	In the book, the following equation is used: <math>ln(y) = \beta_{1} + \beta_{2} ln(t)\,\!</math>. It in fact is a power equation <math>y = bt^{a}\,\!</math> with <math>ln(b) = \beta_{1}\,\!</math> and <math>a = \beta_{2}\,\!</math>. This degradation equation is used for each test unit to predict the pseudo failure time, and then a lognormal distribution is used to model the pseudo failure times. The results are:		In the book, the following equation is used: <math>ln(y) = \beta_{1} + \beta_{2} ln(t)\,\!</math>. It in fact is a power equation <math>y = bt^{a}\,\!</math> with <math>ln(b) = \beta_{1}\,\!</math> and <math>a = \beta_{2}\,\!</math>. This degradation equation is used for each test unit to predict the pseudo failure time, and then a lognormal distribution is used to model the pseudo failure times. The results are:

	* ~~For~~ the power regression model		* The parameters of the power regression model for each unit are:
	:* For unit 1 <math>\beta_{1}\,\!</math> = -2.413 , <math>\beta_{2}\,\!</math> = 0.524		:* For unit 1: <math>\beta_{1}\,\!</math> = -2.413 , <math>\beta_{2}\,\!</math> = 0.524
	:* For unit 2 <math>\beta_{1}\,\!</math> = -2.735 , <math>\beta_{2}\,\!</math> = 0.525		:* For unit 2: <math>\beta_{1}\,\!</math> = -2.735 , <math>\beta_{2}\,\!</math> = 0.525
	:* For unit 3 <math>\beta_{1}\,\!</math> = -2.056 , <math>\beta_{2}\,\!</math> = 0.424		:* For unit 3: <math>\beta_{1}\,\!</math> = -2.056 , <math>\beta_{2}\,\!</math> = 0.424
	:* For unit 4 <math>\beta_{1}\,\!</math> = -2.796 , <math>\beta_{2}\,\!</math> = 0.465		:* For unit 4: <math>\beta_{1}\,\!</math> = -2.796 , <math>\beta_{2}\,\!</math> = 0.465
	:* For unit 5 <math>\beta_{1}\,\!</math> = -2.217 , <math>\beta_{2}\,\!</math> = 0.383		:* For unit 5: <math>\beta_{1}\,\!</math> = -2.217 , <math>\beta_{2}\,\!</math> = 0.383

	* The predicted pseudo failure times: 17,553; 31,816; 75,809; 138,229.		* The predicted pseudo failure times are: 17,553; 31,816; 75,809; 138,229.

	* The fitted lognormal distribution: Ln-Mean = 11.214, Ln-Std = 1.085.		* The parameters of the fitted lognormal distribution are: Ln-Mean = 11.214, Ln-Std = 1.085.


	{{Reference_Example_Heading4}}		{{Reference_Example_Heading4}}

	* ~~For~~ the power regression model:		* The following picture shows the parameters of the power regression model for each unit.

	[[Image:DA_pwr_model.png\|center]]		[[Image:DA_pwr_model.png\|center]]


	* The predicted pseudo failure times:		* The predicted pseudo failure times are shown next.

	[[Image:DA_extrapolated.png\|center]]		[[Image:DA_extrapolated.png\|center]]


	* The fitted lognormal distribution:		* The next picture shows the parameters of the fitted lognormal distribution.

	[[Image:DA_log_model.png\|center]]		[[Image:DA_log_model.png\|center]]

Kate Racaza: Created page with '{{Reference Example}} This example compares the results for a degradation analysis with a power regression model. {{Reference_Example_Heading1}} The data set is from Example …'

2014-06-05T21:50:08Z

Created page with '{{Reference Example}} This example compares the results for a degradation analysis with a power regression model. {{Reference_Example_Heading1}} The data set is from Example …'

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{{Reference Example}}

This example compares the results for a degradation analysis with a power regression model.

{{Reference_Example_Heading1}}

The data set is from Example 8.1 on page 336 in the book ''Life Cycle Reliability Engineering'' by Dr. Guangbin Yang, John Wiley & Sons, 2007.

{{Reference_Example_Heading2}}

The following table shows the percent transconductance degradation data taken at different times for five units of a MOS field-effect transistor. The failure criterion is defined as a degradation greater than or equal to 15%.

{| {{table}}
! Time
!1
!2
!3
!4
!5
|-
| 100||1.05||0.58||0.86||0.6||0.62
|-
| 200||1.4||0.9||1.25||0.6||0.64
|-
| 300||1.75||1.2||1.45||0.6||1.25
|-
| 400||2.1||1.75||1.75||0.9||1.3
|-
| 500||2.1||2.01||1.75||0.9||0.95
|-
| 600||2.8||2||2||1.2||1.25
|-
| 700||2.8||2||2||1.5||1.55
|-
| 800||2.8||2||2||1.5||1.9
|-
| 900||3.2||2||2.3||1.5||1.25
|-
| 1000||3.4||2.3||2.3||1.7||1.55
|-
| 1200||3.8||2.6||2.6||2.1||1.5
|-
| 1400||4.2||2.9||2.8||2.1||1.55
|-
| 1600||4.2||3.2||3.15||1.8||1.9
|-
| 1800||4.5||3.6||3.2||2.1||1.85
|-
| 2000||4.9||3.8||3.2||2.1||2.2
|-
| 2500||5.6||4.2||3.8||2.4||2.2
|-
| 3000||5.9||4.4||3.8||2.7||2.5
|-
| 3500||6.3||4.8||4||2.7||2.2
|-
| 4000||6.6||5||4.2||3||2.8
|-
| 4500||7||5.6||4.4||3||2.8
|-
| 5000||7.8||5.9||4.6||3||2.8
|-
| 6000||8.6||6.2||4.9||3.6||3.1
|-
| 7000||9.1||6.8||5.2||3.6||3.1
|-
| 8000||9.5||7.4||5.8||4.2||3.1
|-
| 9000||10.5||7.7||6.1||4.6||3.7
|-
| 10000||11.1||8.4||6.3||4.2||4.4
|-
| 12000||12.2||8.9||7||4.8||3.7
|-
| 14000||13||9.5||7.2||5.1||4.4
|-
| 16000||14||10||7.6||4.8||4.4
|-
| 18000||15||10.4||7.7||5.3||4.1
|-
| 20000||16||10.9||8.1||5.8||4.1
|-
| 25000||18.5||12.6||8.9||5.7||4.7
|-
| 30000||20.3||13.2||9.5||6.2||4.7
|-
| 35000||22.1||15.4||11.2||8||6.4
|-
| 40000||24.2||18.1||14||10.9||9.4
|-
|}

{{Reference_Example_Heading3}}

In the book, the following equation is used: <math>ln(y) = \beta_{1} + \beta_{2} ln(t)\,\!</math>. It in fact is a power equation <math>y = bt^{a}\,\!</math> with <math>ln(b) = \beta_{1}\,\!</math> and <math>a = \beta_{2}\,\!</math>. This degradation equation is used for each test unit to predict the pseudo failure time, and then a lognormal distribution is used to model the pseudo failure times. The results are:

* For the power regression model
:* For unit 1 <math>\beta_{1}\,\!</math> = -2.413 , <math>\beta_{2}\,\!</math> = 0.524
:* For unit 2 <math>\beta_{1}\,\!</math> = -2.735 , <math>\beta_{2}\,\!</math> = 0.525
:* For unit 3 <math>\beta_{1}\,\!</math> = -2.056 , <math>\beta_{2}\,\!</math> = 0.424
:* For unit 4 <math>\beta_{1}\,\!</math> = -2.796 , <math>\beta_{2}\,\!</math> = 0.465
:* For unit 5 <math>\beta_{1}\,\!</math> = -2.217 , <math>\beta_{2}\,\!</math> = 0.383

* The predicted pseudo failure times: 17,553; 31,816; 75,809; 138,229.

* The fitted lognormal distribution: Ln-Mean = 11.214, Ln-Std = 1.085.

{{Reference_Example_Heading4}}

* For the power regression model:

[[Image:DA_pwr_model.png|center]]

* The predicted pseudo failure times:

[[Image:DA_extrapolated.png|center]]

* The fitted lognormal distribution:

[[Image:DA_log_model.png|center]]