Template:Acb on time: 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: | ||
<br> | |||
::<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> |
Revision as of 01:00, 14 February 2012
Confidence Bounds on Time
The bounds on time (ML estimate of time) for a given reliability are estimated by first solving the reliability function with respect to time:
- [math]\displaystyle{ \widehat{T}=-\widehat{m}\cdot \ln (R) }[/math]
The corresponding confidence bounds are then estimated from:
- [math]\displaystyle{ \begin{align} & {{T}_{U}}= -{{m}_{U}}\cdot \ln (R) \\ & {{T}_{L}}= -{{m}_{L}}\cdot \ln (R) \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]