Weibull++ Standard Folio Data Lognormal: Difference between revisions

Revision as of 19:09, 11 November 2011

Reliability Web Notes
Weibull Folio
Life Data Analysis
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.
The pdf is given by: [math]\displaystyle{ f({T}')=\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{{T}^{\prime }}-{\mu }'}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}} }[/math] where, [math]\displaystyle{ {T}'=\ln (T) }[/math] the natural logarithm of the time-to-failure and [math]\displaystyle{ \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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-The lognormal distribution is a two-parameter distribution with parameters  <br>
+The ''pdf'' is given by: <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>
-::<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>