Template:Acb on time: Difference between revisions

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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 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]