Template:Acb on time: Difference between revisions
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| Line 11: | Line 11: | ||
<br> | <br> | ||
::<math>\begin{align} | ::<math>\begin{align} | ||
& {{T}_{U}}= | & {{T}_{U}}= -{{m}_{U}}\cdot \ln (R) \\ | ||
& {{T}_{L}}= | & {{T}_{L}}= -{{m}_{L}}\cdot \ln (R) | ||
\end{align}</math> | \end{align}</math> | ||
where <math>{{m}_{U}}</math> and <math>{{m}_{L}}</math> are estimated using Eqns. (ArrhuUpper) and (ArrhuLower). | where <math>{{m}_{U}}</math> and <math>{{m}_{L}}</math> are estimated using Eqns. (ArrhuUpper) and (ArrhuLower). | ||
Revision as of 00:59, 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 using Eqns. (ArrhuUpper) and (ArrhuLower).