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| '''Lognormal Distribution General Example Complete Data Unbiased MLE'''
| | #REDIRECT [[The Lognormal Distribution]] |
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| From [[Appendix: Weibull References|Kececioglu [19, p. 406]]]. Nine identical units are tested continuously to failure and their times-to-failure were recorded at 30.4, 36.7, 53.3, 58.5, 74.0, 99.3, 114.3, 140.1, and 257.9 hours.
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| '''Solution'''
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| The results published were obtained by using the unbiased model.
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| Published Results (using MLE):
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| ::<math>\begin{matrix}
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| {{\widehat{\mu }}^{\prime }}=4.3553 \\
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| {{\widehat{\sigma' }}}=0.67677 \\
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| \end{matrix}</math>
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| This same data set can be entered into Weibull++ by creating a data sheet capable of handling non-grouped time-to-failure data. Since the results shown above are unbiased, the Use Unbiased Std on Normal Data option in the User Setup must be selected in order to duplicate these results.
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| Weibull++ computed parameters for maximum likelihood are:
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| ::<math>\begin{matrix}
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| {{\widehat{\mu }}^{\prime }}=4.3553 \\
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| {{\widehat{\sigma' }}}=0.6768 \\
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| \end{matrix}</math>
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