Degradation Data Analysis with a Power Regression Model: Difference between revisions
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{{Reference Example}} | {{Reference Example}} | ||
This example | This example validates the results for a degradation analysis with a power regression model in Weibull++ degradation folios. | ||
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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: | ||
* | * 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}} | ||
* | * 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]] | ||
Latest revision as of 16:22, 28 September 2015
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