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| ====Reliable Life====
| | #REDIRECT [[Eyring_Relationship#Eyring-Lognormal]] |
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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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| ::<math>T_{R}^{\prime }=-\ln (V)-A+\frac{B}{V}+z\cdot {{\sigma }_{{{T}'}}}</math>
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| :where:
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| ::<math>z={{\Phi }^{-1}}\left[ F\left( T_{R}^{\prime },V \right) \right]</math>
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| :and:
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| ::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{z({T}',V)}{{e}^{-\tfrac{{{t}^{2}}}{2}}}dt</math>
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| Since <math>{T}'=\ln (T)</math> the reliable life, <math>{{t}_{R,}}</math> is given by:
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| ::<math>{{t}_{R}}={{e}^{T_{R}^{\prime }}}</math>
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