Template:Example:Eyring: Difference between revisions
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===Eyring-Weibull Example=== | ===Eyring-Weibull Example=== | ||
Consider the following times-to-failure data at three different stress levels. | Consider the following times-to-failure data at three different stress levels. | ||
[[Image:6stresstimefailed.png|center|300px|''Pdf'' of the lognormal distribution with different log-std values.]] | [[Image:6stresstimefailed.png|center|300px|''Pdf'' of the lognormal distribution with different log-std values.]] | ||
The data set was analyzed jointly and with a complete MLE solution over the entire data set using ReliaSoft's ALTA yielding: | The data set was analyzed jointly and with a complete MLE solution over the entire data set using ReliaSoft's ALTA yielding: | ||
::<math>\widehat{\beta }=4.29186497</math> | ::<math>\widehat{\beta }=4.29186497</math> | ||
::<math>\widehat{A}=-11.08784624</math> | ::<math>\widehat{A}=-11.08784624</math> | ||
::<math>\widehat{B}=1454.08635742</math> | ::<math>\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 323K using: | 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 323K using: | ||
::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math> | ::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math> | ||
or: | or: | ||
::<math>\begin{align} | ::<math>\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 | & \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> | \end{align}</math> | ||
Revision as of 01:25, 9 August 2012
Eyring-Weibull Example
Consider the following times-to-failure data at three different stress levels.
The data set was analyzed jointly and with a complete MLE solution over the entire data set using ReliaSoft's ALTA 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 323K 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]