Template:Aae mean: Difference between revisions
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::<math>\begin{align} | ::<math>\begin{align} | ||
\overline{T}=\int_{0}^{\infty }t\cdot f(t,V)dt=\int_{0}^{\infty }t\cdot \frac{1}{C{{e}^{\tfrac{B}{V}}}}{{e}^{-\tfrac{t}{C{{e}^{\tfrac{B}{V}}}}}}dt = C{{e}^{\tfrac{B}{V}}} | \overline{T}=\int_{0}^{\infty }t\cdot f(t,V)dt=\int_{0}^{\infty }t\cdot \frac{1}{C{{e}^{\tfrac{B}{V}}}}{{e}^{-\tfrac{t}{C{{e}^{\tfrac{B}{V}}}}}}dt =\ C{{e}^{\tfrac{B}{V}}} | ||
\end{align}</math> | \end{align}</math> | ||
<br> | <br> | ||
Revision as of 22:30, 13 February 2012
Mean or MTTF
The mean, [math]\displaystyle{ \overline{T}, }[/math] or Mean Time To Failure (MTTF) of the Arrhenius-exponential is given by,
- [math]\displaystyle{ \begin{align} \overline{T}=\int_{0}^{\infty }t\cdot f(t,V)dt=\int_{0}^{\infty }t\cdot \frac{1}{C{{e}^{\tfrac{B}{V}}}}{{e}^{-\tfrac{t}{C{{e}^{\tfrac{B}{V}}}}}}dt =\ C{{e}^{\tfrac{B}{V}}} \end{align} }[/math]