Eyring Example: Difference between revisions
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{ | <noinclude>{{Banner_ALTA_Examples}} | ||
''This example appears in the [https://help.reliasoft.com/reference/accelerated_life_testing_data_analysis Accelerated life testing reference].'' | |||
Consider the following times-to-failure data at three different stress levels. | </noinclude>Consider the following times-to-failure data at three different stress levels. | ||
[[Image:6stresstimefailed.png|center|350px|''Pdf'' of the lognormal distribution with different log-std values.]] | |||
[[Image:6stresstimefailed.png|center| | |||
The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull model, yielding: | |||
: | |||
::<math>\widehat{\beta }=4.29186497\,\!</math> | |||
::<math>\widehat{ | |||
::<math>\widehat{A}=-11.08784624\,\!</math> | |||
::<math>\widehat{ | |||
< | ::<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 323 K by using: | ||
::<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> | ||
Latest revision as of 19:02, 18 September 2023
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This example appears in the Accelerated life testing reference.
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 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]