Template:Lognormal distribution mean

The Mean or MTTF

The mean of the lognormal distribution, [math]\displaystyle{ \mu }[/math] , is given by [18]:

[math]\displaystyle{ \mu ={{e}^{{\mu }'+\tfrac{1}{2}\sigma _{{{T}'}}^{2}}} }[/math]

The mean of the natural logarithms of the times-to-failure, [math]\displaystyle{ \mu' }[/math] , in terms of [math]\displaystyle{ \bar{T} }[/math] and [math]\displaystyle{ {{\sigma }_{T}} }[/math] is givgen by:

[math]\displaystyle{ {\mu }'=\ln \left( {\bar{T}} \right)-\frac{1}{2}\ln \left( \frac{\sigma _{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right) }[/math]