Weibull-Bayesian with Prior Information on Beta: Difference between revisions
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Kate Racaza (talk | contribs) (Created page with '{{Reference Example}} This example compares the Weibull-Bayesian calculation. {{Reference_Example_Heading1}} The data from Example 14.1 on page 348 in the book ''Statistical …') |
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{{Reference Example}} | {{Reference Example}} | ||
This example | This example validates the Weibull-Bayesian calculations in Weibull++ standard folios. | ||
{{Reference_Example_Heading1}} | {{Reference_Example_Heading1}} | ||
The data from Example 14.1 on page 348 in the book ''Statistical Methods for Reliability Data'' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998 is used. | The data set from Example 14.1 on page 348 in the book ''Statistical Methods for Reliability Data'' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998 is used. | ||
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{{Reference_Example_Heading4}} | {{Reference_Example_Heading4}} | ||
In Weibull++, the prior distribution is set for <math>\beta\,\!</math> directly. Based on the information of <math>\sigma\,\!</math>, we know <math>\beta_{0.005}\,\!</math> = 2 and <math>\beta_{0.995}\,\!</math> = 5. Therefore, we can get the prior lognormal distribution for <math>\beta\,\!</math>. | In Weibull++, the prior distribution is set for <math>\beta\,\!</math> directly. Based on the information of <math>\sigma\,\!</math>, we know <math>\beta_{0.005}\,\!</math> = 2 and <math>\beta_{0.995}\,\!</math> = 5. Therefore, we can use the Quick Parameter Estimator (QPE) to get the prior lognormal distribution for <math>\beta\,\!</math>. The results are Log-Mean = 1.15129 and Log-Std = 0.17786, as shown next. | ||
[[Image: | [[Image:WeiBays_QPE.png|center|550px|]] | ||
Applying this prior distribution for Wei-Bayesian, we have the following results: | Applying this prior distribution for Wei-Bayesian, we have the following results: | ||
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* The 95% two-sided Bayesian confidence interval for <math>t_{0.05}\,\!</math> (B5% life) is [1623, 3452]. | * The 95% two-sided Bayesian confidence interval for <math>t_{0.05}\,\!</math> (B5% life) is [1623, 3452]. | ||
[[Image: | [[Image:WeiBays_B5.png|center|550px|]] | ||
* The 95% two-sided Bayesian confidence interval for <math>t_{0.10}\,\!</math> (B10% life) is [2030, 4763]. | * The 95% two-sided Bayesian confidence interval for <math>t_{0.10}\,\!</math> (B10% life) is [2030, 4763]. | ||
[[Image: | [[Image:WeiBays_B10.png|center|550px|]] | ||
* The 95% two-sided Bayesian confidence interval for F(2000) (probability of failure at time of 2000) is [0.014, 0.095]. | * The 95% two-sided Bayesian confidence interval for F(2000) (probability of failure at time of 2000) is [0.014, 0.095]. | ||
[[Image: | [[Image:WeiBays_F2000.png|center|550px|]] | ||
* The 95% two-sided Bayesian confidence interval for F(5000) (probability of failure at time of 5000) is [0.111, 0.903]. | * The 95% two-sided Bayesian confidence interval for F(5000) (probability of failure at time of 5000) is [0.111, 0.903]. | ||
[[Image: | [[Image:WeiBays_F5000.png|center|550px|]] | ||
The results in Weibull++ are very close | The results in Weibull++ are very close but not exactly the same as the results in the book. The differences are mainly caused by the fact that the prior lognormal distribution is for <math>\sigma\,\!</math> in the book while it is for <math>\beta\,\!</math> in Weibull++. | ||
Latest revision as of 16:21, 28 September 2015
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