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| | #REDIRECT [[Template:WebNotes/Weibull%2B%2BStandard_Folio_Data_Lognormal]] |
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| | align="center" valign="middle" |{{Font|Weibull Folio- Lognormal|11|tahoma|bold|gray}}
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| | align="center" valign="middle" | {{Font|Life Data Analysis|10|tahoma|bold|gray}}
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| The lognormal distribution is commonly used to model the lives of units whose failure modes are of a fatigue-stress nature. It has an increasing failure rate behavior and then decreasing towards the end of life.
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| The ''pdf'' is given by: <br>
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| <math>f({T}')=\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{{T}^{\prime }}-{\mu }'}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}</math>
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| <br> where,
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| <br><math>{T}'=\ln (T)</math><br>
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| the natural logarithm of the time-to-failure and
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| <br><math>\mu' \text{ and } \sigma_{T'}</math><br>
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| are the mean and standard deviation of of the natural logarithms of the times-to-failure.
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| | align="center" valign="middle" | [http://reliawiki.com/index.php/Template:Lognormal_distribution Lognormal Distribution]
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| | align="center" valign="middle" | [http://www.reliawiki.com/index.php/Weibull_Examples_Lognormal See Examples...]
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