Template:Alta al rl

Reliable Life
For the Arrhenius-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:
 * $${{T}'_{R}}= ln(C)+\frac{B}{V}+z \cdot {{\sigma}_{{T}'}}$$

where:


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

and:


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

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


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