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| '''Lognormal Distribution General Example Complete Data RRX'''
| | #REDIRECT [[The Lognormal Distribution]] |
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| From [[Appendix: Weibull References|Kececioglu [20, p. 347]]]. Fifteen identical units were tested to failure and following is a table of their times-to-failure:
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| <center><math>\text{Table }\text{ - Times-to-Failure Data}</math></center>
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| <center><math>\begin{matrix}
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| \text{Data Point Index} & \text{Time-to-Failure, hr} \\
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| \text{1} & \text{62}\text{.5} \\
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| \text{2} & \text{91}\text{.9} \\
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| \text{3} & \text{100}\text{.3} \\
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| \text{4} & \text{117}\text{.4} \\
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| \text{5} & \text{141}\text{.1} \\
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| \text{6} & \text{146}\text{.8} \\
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| \text{7} & \text{172}\text{.7} \\
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| \text{8} & \text{192}\text{.5} \\
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| \text{9} & \text{201}\text{.6} \\
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| \text{10} & \text{235}\text{.8} \\
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| \text{11} & \text{249}\text{.2} \\
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| \text{12} & \text{297}\text{.5} \\
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| \text{13} & \text{318}\text{.3} \\
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| \text{14} & \text{410}\text{.6} \\
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| \text{15} & \text{550}\text{.5} \\
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| \end{matrix}</math></center>
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| '''Solution'''
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| Published results (using probability plotting):
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| ::<math>\begin{matrix}
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| {{\widehat{\mu }}^{\prime }}=5.22575 \\
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| {{\widehat{\sigma' }}}=0.62048. \\
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| \end{matrix}</math>
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| Weibull++ computed parameters for rank regression on X are:
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| ::<math>\begin{matrix}
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| {{\widehat{\mu }}^{\prime }}=5.2303 \\
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| {{\widehat{\sigma'}}}=0.6283. \\
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| \end{matrix}</math>
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| The small differences are due to the precision errors when fitting a line manually, whereas in Weibull++ the line was fitted mathematically.
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