Template:Aae mean: Difference between revisions

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(Created page with '====Mean or MTTF==== <br> The mean, <math>\overline{T},</math> or Mean Time To Failure (MTTF) of the Arrhenius-exponential is given by, <br> ::<math>\begin{align} & \overli…')
 
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::<math>\begin{align}
::<math>\begin{align}
  & \overline{T}= & \mathop{}_{0}^{\infty }t\cdot f(t,V)dt=\mathop{}_{0}^{\infty }t\cdot \frac{1}{C{{e}^{\tfrac{B}{V}}}}{{e}^{-\tfrac{t}{C{{e}^{\tfrac{B}{V}}}}}}dt \\
  \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}}}   
  & = & C{{e}^{\tfrac{B}{V}}}   
\end{align}</math>
\end{align}</math>


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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]