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| ====Reliable Life====
| | #REDIRECT [[Arrhenius_Relationship#Arrhenius-Lognormal_Statistical_Properties_Summary]] |
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| For the Arrhenius-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}}= ln(C)+\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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