Eyring Example: Difference between revisions
Kate Racaza (talk | contribs) m (updated banner) |
No edit summary |
||
| Line 1: | Line 1: | ||
<noinclude>{{Banner_ALTA_Examples}} | <noinclude>{{Banner_ALTA_Examples}} | ||
</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|400px|''Pdf'' of the lognormal distribution with different log-std values.]] | [[Image:6stresstimefailed.png|center|400px|''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> | ||
::<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 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> | ||
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 07:39, 7 August 2012
 |
New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.
As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at ALTA examples and ALTA reference examples.
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]