Template:Eyring-log rl: Difference between revisions

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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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Latest revision as of 23:40, 16 August 2012

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