Template:Acb on reliability: Difference between revisions
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where <math>{{m}_{U}}</math> and <math>{{m}_{L}}</math> are estimated | where <math>{{m}_{U}}</math> and <math>{{m}_{L}}</math> are estimated estimated by: | ||
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::<math>\begin{align} | |||
& {{m}_{U}}= \widehat{m}\cdot {{e}^{\tfrac{{{K}_{\alpha }}\sqrt{Var(\widehat{m})}}{\widehat{m}}}} \\ | |||
& {{m}_{L}}= \widehat{m}\cdot {{e}^{-\tfrac{{{K}_{\alpha }}\sqrt{Var(\widehat{m})}}{\widehat{m}}}} | |||
\end{align}</math> | |||
<br> | <br> | ||
Revision as of 00:58, 14 February 2012
Confidence Bounds on Reliability
The bounds on reliability for any given time, [math]\displaystyle{ T }[/math] , are estimated by:
- [math]\displaystyle{ \begin{align} & {{R}_{U}}(T)= & {{e}^{-\tfrac{T}{{{m}_{U}}}}} \\ & {{R}_{L}}(T)= & {{e}^{-\tfrac{T}{{{m}_{L}}}}} \end{align} }[/math]
where [math]\displaystyle{ {{m}_{U}} }[/math] and [math]\displaystyle{ {{m}_{L}} }[/math] are estimated estimated by:
- [math]\displaystyle{ \begin{align} & {{m}_{U}}= \widehat{m}\cdot {{e}^{\tfrac{{{K}_{\alpha }}\sqrt{Var(\widehat{m})}}{\widehat{m}}}} \\ & {{m}_{L}}= \widehat{m}\cdot {{e}^{-\tfrac{{{K}_{\alpha }}\sqrt{Var(\widehat{m})}}{\widehat{m}}}} \end{align} }[/math]