Weibull++ Standard Folio Data Lognormal

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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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