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| ===Eyring-Lognormal Statistical Properties Summary===
| | #REDIRECT [[Eyring_Relationship#Eyring-Lognormal]] |
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| {{eyring-log mean}}
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| {{eyring-log median}}
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| {{eyring-log sd}}
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| {{eyring-log mode}}
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| {{eyring-log rf}}
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| ====Reliable Life====
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| <br>
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| For the Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is estimated by first solving the reliability equation with respect to time, as follows:
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| <br>
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| ::<math>T_{R}^{\prime }=-\ln (V)-A+\frac{B}{V}+z\cdot {{\sigma }_{{{T}'}}}</math>
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| <br>
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| :where:
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| <br>
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| ::<math>z={{\Phi }^{-1}}\left[ F\left( T_{R}^{\prime },V \right) \right]</math>
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| <br>
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| :and:
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| <br>
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| ::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\mathop{}_{-\infty }^{z({T}',V)}{{e}^{-\tfrac{{{t}^{2}}}{2}}}dt</math>
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| <br>
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| <br>
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| Since <math>{T}'=\ln (T)</math> the reliable life, <math>{{t}_{R,}}</math> is given by:
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| <br>
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| ::<math>{{t}_{R}}={{e}^{T_{R}^{\prime }}}</math>
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| ====Eyring-Lognormal Failure Rate====
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| <br>
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| The Eyring-lognormal failure rate is given by:
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| ::<math>\lambda (T,V)=\frac{f(T,V)}{R(T,V)}=\frac{\tfrac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'+\ln (V)+A-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}}{\mathop{}_{{{T}'}}^{\infty }\tfrac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'+\ln (V)+A-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt}</math>
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