Template:Ald mean

The Mean or MTTF

• The mean of the lognormal distribution, [math]\displaystyle{ \bar{T} }[/math], is given by:

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

• The mean of the natural logarithms of the failure times, [math]\displaystyle{ {{\bar{T}}^{^{\prime }}} }[/math], in terms of [math]\displaystyle{ \bar{T} }[/math] and [math]\displaystyle{ {{\sigma }_{T}} }[/math] is given by:

[math]\displaystyle{ {{\bar{T}}^{\prime }}=\ln \left( {\bar{T}} \right)-\frac{1}{2}\ln \left( \frac{\sigma _{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right) }[/math]