Template:Example: Lognormal General Example Complete Data Unbiased MLE: Difference between revisions

Latest revision as of 07:56, 14 August 2012

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-'''Lognormal Distribution General Example Complete Data Unbiased MLE'''
+#REDIRECT [[The Lognormal Distribution]]
-From 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.
-'''Solution'''
-The results published were obtained by using the unbiased model.
-Published Results (using MLE):
-::<math>\begin{matrix}
-   {{\widehat{\mu }}^{\prime }}=4.3553  \\
-   {{\widehat{\sigma }}_{{{T}'}}}=0.67677  \\
-\end{matrix}</math>
-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.
-Weibull++ computed parameters for maximum likelihood are:
-::<math>\begin{matrix}
-   {{\widehat{\mu }}^{\prime }}=4.3553  \\
-   {{\widehat{\sigma }}_{{{T}'}}}=0.6768  \\
-\end{matrix}</math>