Template:Eyring-log sd: Difference between revisions

Latest revision as of 23:36, 16 August 2012

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-====The Standard Deviation====
+#REDIRECT [[Eyring_Relationship#Eyring-Lognormal]]
-<br>
-•	The standard deviation of the Eyring-lognormal model (standard deviation of the times-to-failure),  <math>{{\sigma }_{T}}</math> , is given by:
-<br>
-::<math>\begin{align}
-  & {{\sigma }_{T}}= & \sqrt{\left( {{e}^{2\bar{{T}'}+\sigma _{{{T}'}}^{2}}} \right)\left( {{e}^{\sigma _{{{T}'}}^{2}}}-1 \right)} \\
- & = & \sqrt{\left( {{e}^{2\left( -\ln (V)-A+\tfrac{B}{V} \right)+\sigma _{{{T}'}}^{2}}} \right)\left( {{e}^{\sigma _{{{T}'}}^{2}}}-1 \right)}
-\end{align}</math>
-<br>
-•	The standard deviation of the natural logarithms of the times-to-failure,  <math>{{\sigma }_{{{T}'}}}</math> , in terms of  <math>\bar{T}</math>  and  <math>{{\sigma }_{T}}</math>  is given by:
-<br>
-::<math>{{\sigma }_{{{T}'}}}=\sqrt{\ln \left( \frac{\sigma _{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>