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