Template:Eyring-log rl

Reliable Life
For the Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, $${{t}_{R}},$$  is estimated by first solving the reliability equation with respect to time, as follows:


 * $$T_{R}^{\prime }=-\ln (V)-A+\frac{B}{V}+z\cdot {{\sigma }_}$$


 * where:


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


 * and:


 * $$\Phi (z)=\frac{1}{\sqrt{2\pi }}\mathop{}_{-\infty }^{z({T}',V)}{{e}^{-\tfrac{2}}}dt$$

Since $${T}'=\ln (T)$$  the reliable life,  $${{t}_{R,}}$$  is given by:


 * $${{t}_{R}}={{e}^{T_{R}^{\prime }}}$$