Template:Acb on time: Difference between revisions

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====Confidence Bounds on Time====
#REDIRECT [[Arrhenius_Relationship#Approximate_Confidence_Bounds_for_the_Arrhenius-Exponential]]
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The bounds on time (ML estimate of time) for a given reliability are estimated by first solving the reliability function with respect to time:
 
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::<math>\widehat{T}=-\widehat{m}\cdot \ln (R)</math>
 
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The corresponding confidence bounds are then estimated from:
 
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::<math>\begin{align}
  & {{T}_{U}}= -{{m}_{U}}\cdot \ln (R) \\
& {{T}_{L}}= -{{m}_{L}}\cdot \ln (R) 
\end{align}</math>
 
 
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>
 
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Latest revision as of 05:50, 16 August 2012