Eyring Example

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Consider the following times-to-failure data at three different stress levels.

The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull relationship model, yielding:

[math]\displaystyle{ \widehat{\beta }=4.29186497 }[/math]

[math]\displaystyle{ \widehat{A}=-11.08784624 }[/math]

[math]\displaystyle{ \widehat{B}=1454.08635742 }[/math]

Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K by using:

[math]\displaystyle{ \overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right) }[/math]

or:

[math]\displaystyle{ \begin{align} & \overline{T}= & \frac{1}{323}{{e}^{-\left( -11.08784624-\tfrac{1454.08635742}{323} \right)}}\cdot \Gamma \left( \frac{1}{4.29186497}+1 \right) =16,610\text{ }hr \end{align} }[/math]