Template:Eyring-log mean

The Mean
The mean life of the Eyring-lognormal model (mean of the times-to-failure), $$\bar{T}$$, is given by:


 * $$\begin{align}

\bar{T}=\ {{e}^{\bar{{T}'}+\tfrac{1}{2}\sigma _^{2}}} =\ {{e}^{-\ln (V)-A+\tfrac{B}{V}+\tfrac{1}{2}\sigma _^{2}}} \end{align}$$ The mean of the natural logarithms of the times-to-failure, $${{\bar{T}}^{^{\prime }}}$$, in terms of  $$\bar{T}$$  and  $${{\sigma }_{T}}$$  is given by:
 * $${{\bar{T}}^{\prime }}=\ln \left( {\bar{T}} \right)-\frac{1}{2}\ln \left( \frac{\sigma _{T}^{2}}+1 \right)$$