Weibull++ Standard Folio Data Lognormal

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 lognormal distribution is a two-parameter distribution with parameters [math]\displaystyle{ {\mu }' }[/math] and [math]\displaystyle{ {{\sigma }_{{{T}'}}} }[/math] . The [math]\displaystyle{ pdf }[/math] for this distribution 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]. , where the [math]\displaystyle{ T }[/math] values are the times-to-failure, and [math]\displaystyle{ \mu'=\text{mean of the natural logarithms} }[/math] [math]\displaystyle{ \text{of the times-to-failure,} }[/math] [math]\displaystyle{ \sigma_{T'}=\text{standard deviation of the natural logarithms} }[/math] [math]\displaystyle{ \text{of the times-to-failure} }[/math]
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