Degradation Data Analysis with a Linear Regression Model - Revision history

Kate Racaza at 16:23, 28 September 2015

2015-09-28T16:23:19Z

← Older revision		Revision as of 16:23, 28 September 2015
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	{{Reference Example}}		{{Reference Example}}

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

Kate Racaza at 17:03, 9 June 2014

2014-06-09T17:03:42Z

← Older revision		Revision as of 17:03, 9 June 2014
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	{{Reference_Example_Heading2}}		{{Reference_Example_Heading2}}

	The test is for the current (amperage) of a laser device. Failure is defined as a 10% increases in amperage.		The test is for the current (i.e., amperage) of a laser device. Failure is defined as a 10% increases in amperage.

	{\| {{table}}		{\| {{table}}
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	{{Reference_Example_Heading4}}		{{Reference_Example_Heading4}}

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

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


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

	[[Image:DA_linear_extrapolated.png\|center\|]]		[[Image:DA_linear_extrapolated.png\|center\|]]
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	* The fitted Weibull distribution		* The next picture shows the parameters of the fitted Weibull distribution.

	[[Image:DA_linear_plot.png\|center\|550px\|]]		[[Image:DA_linear_plot.png\|center\|550px\|]]

Kate Racaza at 18:41, 6 June 2014

2014-06-06T18:41:56Z

← Older revision		Revision as of 18:41, 6 June 2014
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			* For the power regression model

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


			* The predicted pseudo failure times.

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


			: The predicted failure times in Weibull++ are slightly different from the values given in the book. Since the book does not provide the model parameters, we couldn’t compare the Weibulll++ results with the results in the book.


			* The fitted Weibull distribution

			[[Image:DA_linear_plot.png\|center\|550px\|]]

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

2014-06-06T18:01:58Z

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

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{{Reference Example}}

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

{{Reference_Example_Heading1}}

The data set is from Example 13.10 on page 338 in the book ''Statistical Methods for Reliability Data'' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.

{{Reference_Example_Heading2}}

The test is for the current (amperage) of a laser device. Failure is defined as a 10% increases in amperage.

{| {{table}}
!rowspan="2"|Time
!colspan="15"|Unit Number
|-
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
|-
| 250||0.47||0.71||0.71||0.36||0.27||0.36||0.36||0.46||0.51||0.41||0.44||0.4||0.3||0.44||0.51
|-
| 500||0.93||1.22||1.17||0.62||0.61||1.39||0.92||1.07||0.93||1.79||1||0.8||0.74||0.7||0.83
|-
| 750||2.11||1.9||1.73||1.36||1.11||1.95||1.21||1.42||1.57||2.38||1.57||1.4||1.52||1.05||1.29
|-
| 1000||2.72||2.3||1.99||1.95||1.77||2.86||1.46||1.77||1.96||3||1.96||1.7||1.85||1.35||1.52
|-
| 1250||3.51||2.87||2.53||2.3||2.06||3.46||1.93||2.11||2.59||3.84||2.51||3||2.39||1.8||1.91
|-
| 1500||4.34||3.75||2.97||2.95||2.58||3.81||2.39||2.4||3.29||4.5||2.84||3.6||2.95||2.55||2.27
|-
| 1750||4.91||4.42||3.3||3.39||2.99||4.53||2.68||2.78||3.61||5.25||3.47||4||3.51||2.83||2.78
|-
| 2000||5.48||4.99||3.94||3.79||3.38||5.35||2.94||3.02||4.11||6.26||4.01||4.4||3.92||3.39||3.42
|-
| 2250||5.99||5.51||4.16||4.11||4.05||5.92||3.42||3.29||4.6||7.05||4.51||4.8||5.03||3.72||3.78
|-
| 2500||6.72||6.07||4.45||4.5||4.63||6.17||4.09||3.75||4.91||7.8||4.8||5.2||5.47||4.09||4.11
|-
| 2750||7.13||6.64||4.89||4.72||5.24||7.7||4.58||4.16||5.34||8.32||5.2||5.5||5.84||4.83||4.38
|-
| 3000||8||7.16||5.27||4.98||5.62||8.61||4.84||4.76||5.84||8.93||5.66||6||6.5||5.41||4.63
|-
| 3250||8.92||7.78||5.69||5.28||6.04||9.15||5.11||5.16||6.4||9.55||6.2||6.2||6.94||5.76||5.38
|-
| 3500||9.49||8.42||6.02||5.61||6.32||9.95||5.57||5.46||6.84||10.5||6.54||7||7.39||6.14||5.84
|-
| 3750||9.87||8.91||6.45||5.95||7.1||10.49||6.11||5.81||7.2||11.3||6.96||7.4||7.85||6.51||6.16
|-
| 4000||10.94||9.28||6.88||6.14||7.59||11.01||7.17||6.24||7.88||12.2||7.42||7.9||8.09||6.88||6.62
|-
|}

{{Reference_Example_Heading3}}

The book provides a linear regression model, <math>y=b+at\,\!</math>, but the parameters of the model are not provided. Only the predicted failure times are given. These are: 3702, 4194, 5847, 6172, 5301, 3592, 6051, 6538, 5110, 3306, 5326, 4995, 4721, 5689, and 6102. A Weibull distribution is used to fit the data; however, the model parameters are not provided. Only a probability plot is given.

{{Reference_Example_Heading4}}