Template:Eyring-log rl

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Reliable Life


For the Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, [math]\displaystyle{ {{t}_{R}}, }[/math] is estimated by first solving the reliability equation with respect to time, as follows:


[math]\displaystyle{ T_{R}^{\prime }=-\ln (V)-A+\frac{B}{V}+z\cdot {{\sigma }_{{{T}'}}} }[/math]


where:


[math]\displaystyle{ z={{\Phi }^{-1}}\left[ F\left( T_{R}^{\prime },V \right) \right] }[/math]


and:


[math]\displaystyle{ \Phi (z)=\frac{1}{\sqrt{2\pi }}\mathop{}_{-\infty }^{z({T}',V)}{{e}^{-\tfrac{{{t}^{2}}}{2}}}dt }[/math]



Since [math]\displaystyle{ {T}'=\ln (T) }[/math] the reliable life, [math]\displaystyle{ {{t}_{R,}} }[/math] is given by:


[math]\displaystyle{ {{t}_{R}}={{e}^{T_{R}^{\prime }}} }[/math]