Weibull++ Standard Folio Data Lognormal: Difference between revisions

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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 lognormal distribution is a two-parameter distribution with parameters  <br>
<math>{\mu }'</math>  and  <math>{{\sigma }_{{{T}'}}}</math>. <br> The ''pdf'' is given by:
 
::<math>f({T}')=\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{{T}^{\prime }}-{\mu }'}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}</math>
<br> where,
<br><math>{T}'=\ln (T)</math><br>
the natural logarithm of the time-to-failure  and
<br><math>\mu' \text{ and } \sigma_{T'}</math>\
are the mean and standard deviation of of the natural logarithms of the times-to-failure.
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Latest revision as of 21:10, 10 July 2015

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