Eyring Example: Difference between revisions
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<noinclude>{{Banner_ALTA_Examples}} | <noinclude>{{Banner_ALTA_Examples}} | ||
''This example appears in the [[Eyring_Relationship#Eyring-Weibull|Accelerated Life Testing Data Analysis Reference]] book.'' | |||
</noinclude>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| | [[Image:6stresstimefailed.png|center|350px|''Pdf'' of the lognormal distribution with different log-std values.]] | ||
The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull relationship model, yielding: | The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull relationship model, yielding: | ||
::<math>\widehat{\beta }=4.29186497</math> | ::<math>\widehat{\beta }=4.29186497</math> | ||
| Line 11: | Line 15: | ||
::<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 323 K by 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 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> | ::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math> | ||
Revision as of 01:30, 14 August 2012
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This example appears in the Accelerated Life Testing Data Analysis Reference book.
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]