Template:Example: Lognormal General Example Complete Data Unbiased MLE: Difference between revisions
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'''Lognormal Distribution 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. | 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. | ||
'''Solution''' | '''Solution''' | ||
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::<math>\begin{matrix} | ::<math>\begin{matrix} | ||
{{\widehat{\mu }}^{\prime }}=4.3553 \\ | {{\widehat{\mu }}^{\prime }}=4.3553 \\ | ||
{{\widehat{\sigma | {{\widehat{\sigma' }}}=0.67677 \\ | ||
\end{matrix}</math> | \end{matrix}</math> | ||
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::<math>\begin{matrix} | ::<math>\begin{matrix} | ||
{{\widehat{\mu }}^{\prime }}=4.3553 \\ | {{\widehat{\mu }}^{\prime }}=4.3553 \\ | ||
{{\widehat{\sigma | {{\widehat{\sigma' }}}=0.6768 \\ | ||
\end{matrix}</math> | \end{matrix}</math> | ||
Revision as of 23:46, 13 February 2012
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' }}}=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' }}}=0.6768 \\ \end{matrix} }[/math]