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| ====The Standard Deviation====
| | #REDIRECT [[Arrhenius_Relationship#Arrhenius-Lognormal_Statistical_Properties_Summary]] |
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| • The standard deviation of the Arrhenius-lognormal model (standard deviation of the times-to-failure), <math>{{\sigma }_{T}}</math> , is given by:
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| ::<math>\begin{align}
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| & {{\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 (C)+\tfrac{B}{V} \right)+\sigma _{{{T}'}}^{2}}} \right)\left( {{e}^{\sigma _{{{T}'}}^{2}}}-1 \right)}
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| \end{align}</math>
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| • 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:
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| ::<math>{{\sigma }_{{{T}'}}}=\sqrt{\ln \left( \frac{\sigma _{T}^{2}}{{{{\bar{T}}}^{2}}}+1 \right)}</math>
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