Template:Eyring-log mean: Difference between revisions
Jump to navigation
Jump to search
Line 2: | Line 2: | ||
<br> | <br> | ||
• The mean life of the Eyring-lognormal model (mean of the times-to-failure), <math>\bar{T}</math> , is given by: | • The mean life of the Eyring-lognormal model (mean of the times-to-failure), <math>\bar{T}</math> , is given by: | ||
<br> | <br> | ||
::<math>\begin{align} | ::<math>\begin{align} | ||
\bar{T}=\ {{e}^{\bar{{T}'}+\tfrac{1}{2}\sigma _{{{T}'}}^{2}}} =\ {{e}^{-\ln (V)-A+\tfrac{B}{V}+\tfrac{1}{2}\sigma _{{{T}'}}^{2}}} | \bar{T}=\ {{e}^{\bar{{T}'}+\tfrac{1}{2}\sigma _{{{T}'}}^{2}}} =\ {{e}^{-\ln (V)-A+\tfrac{B}{V}+\tfrac{1}{2}\sigma _{{{T}'}}^{2}}} |
Revision as of 23:51, 27 February 2012
The Mean
• The mean life of the Eyring-lognormal model (mean of the times-to-failure), [math]\displaystyle{ \bar{T} }[/math] , is given by:
- [math]\displaystyle{ \begin{align} \bar{T}=\ {{e}^{\bar{{T}'}+\tfrac{1}{2}\sigma _{{{T}'}}^{2}}} =\ {{e}^{-\ln (V)-A+\tfrac{B}{V}+\tfrac{1}{2}\sigma _{{{T}'}}^{2}}} \end{align} }[/math]
The mean of the natural logarithms of the times-to-failure, [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]