Template:Appr conf bounds for arr-exp: Difference between revisions

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==Approximate Confidence Bounds for the Arrhenius-Exponential==
#REDIRECT [[Arrhenius_Relationship#Approximate_Confidence_Bounds_for_the_Arrhenius-Exponential]]
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There are different methods for computing confidence bounds. ALTA utilizes confidence bounds that are based on the asymptotic theory for maximum likelihood estimates, most commonly referred to as the Fisher matrix bounds.
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{{acb on the mean life}}
 
{{acb on reliability}}
 
===Confidence Bounds on Time===
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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 using Eqns. (ArrhuUpper) and (ArrhuLower).

Latest revision as of 05:47, 16 August 2012

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