Template:App cb 4 the eyring-ex: Difference between revisions

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==Approximate Confidence Bounds for the Eyring-Exponential==
#REDIRECT [[Eyring_Relationship#Eyring_Confidence_Bounds]]
<br>
{{eyring-ex cb on mean life}}
 
===Confidence Bounds on Reliability===
 
The bounds on reliability at a given time,  <math>T</math> , are estimated by:
 
<br>
::<math>\begin{align}
  & {{R}_{U}}= & {{e}^{-\tfrac{T}{{{m}_{U}}}}} \\
&  &  \\
& {{R}_{L}}= & {{e}^{-\tfrac{T}{{{m}_{L}}}}} 
\end{align}</math>
 
<br>
where  <math>{{m}_{U}}</math>  and  <math>{{m}_{L}}</math>  are estimated using Eqns. (EyrxpMeanUpper) and (EyrxpMeanLower).
<br>
===Confidence Bounds on Time===
<br>
The bounds on time (ML estimate of time) for a given reliability are estimated by first solving the reliability function with respect to time:
 
<br>
::<math>\widehat{T}=-\widehat{m}\cdot \ln (R)</math>
 
<br>
The corresponding confidence bounds are estimated from:
 
<br>
::<math>\begin{align}
  & {{T}_{U}}= & -{{m}_{U}}\cdot \ln (R) \\
&  &  \\
& {{T}_{L}}= & -{{m}_{L}}\cdot \ln (R) 
\end{align}</math>
 
<br>
where  <math>{{m}_{U}}</math>  and  <math>{{m}_{L}}</math>  are estimated using Eqns. (EyrxpMeanUpper) and (EyrxpMeanLower).

Latest revision as of 01:00, 17 August 2012

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