Template:Eyring-ex mean: Difference between revisions
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& \overline{T}= & \int_{0}^{\infty }t\cdot f(t,V)dt=\int_{0}^{\infty }t\cdot V{{e}^{\left( A-\tfrac{B}{V} \right)}}{{e}^{-tV{{e}^{\left( A-\tfrac{B}{V} \right)}}}}dt =\ \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} | & \overline{T}= & \int_{0}^{\infty }t\cdot f(t,V)dt=\int_{0}^{\infty }t\cdot V{{e}^{\left( A-\tfrac{B}{V} \right)}}{{e}^{-tV{{e}^{\left( A-\tfrac{B}{V} \right)}}}}dt =\ \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} | ||
\end{align}</math> | \end{align}</math> | ||
<br> | |||
Revision as of 23:41, 27 February 2012
Mean or MTTF
The mean, [math]\displaystyle{ \overline{T}, }[/math] or Mean Time To Failure (MTTF) for the Eyring-exponential is given by:
- [math]\displaystyle{ \begin{align} & \overline{T}= & \int_{0}^{\infty }t\cdot f(t,V)dt=\int_{0}^{\infty }t\cdot V{{e}^{\left( A-\tfrac{B}{V} \right)}}{{e}^{-tV{{e}^{\left( A-\tfrac{B}{V} \right)}}}}dt =\ \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} \end{align} }[/math]