Template:Eyring-log sd

The Standard Deviation
The standard deviation of the Eyring-lognormal model (standard deviation of the times-to-failure), $${{\sigma }_{T}}$$, is given by:


 * $$\begin{align}

& {{\sigma }_{T}}= & \sqrt{\left( {{e}^{2\bar{{T}'}+\sigma _^{2}}} \right)\left( {{e}^{\sigma _^{2}}}-1 \right)} =\ \sqrt{\left( {{e}^{2\left( -\ln (V)-A+\tfrac{B}{V} \right)+\sigma _^{2}}} \right)\left( {{e}^{\sigma _^{2}}}-1 \right)} \end{align}$$

The standard deviation of the natural logarithms of the times-to-failure, $${{\sigma }_}$$, in terms of  $$\bar{T}$$  and  $${{\sigma }_{T}}$$  is given by:


 * $${{\sigma }_}=\sqrt{\ln \left( \frac{\sigma _{T}^{2}}+1 \right)}$$