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.  
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>
The ''pdf'' is given by: <br>
<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>
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are the mean and standard deviation of of the natural logarithms of the times-to-failure.
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]
| valign="middle" | [http://reliawiki.com/index.php/Template:Lognormal_distribution Lognormal Distribution]


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Revision as of 20:39, 8 February 2012

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Weibull Folio- Lognormal
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.

Lognormal Distribution


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