Template:Example: Lognormal General Example Complete Data Unbiased MLE

Lognormal Distribution General Example Complete Data Unbiased MLE

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]\displaystyle{ \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]\displaystyle{ \begin{matrix} {{\widehat{\mu }}^{\prime }}=4.3553 \\ {{\widehat{\sigma }}_{{{T}'}}}=0.6768 \\ \end{matrix} }[/math]