Template:Eyring-ex rl

Reliable Life
For the Eyring-exponential model, the reliable life, or the mission duration for a desired reliability goal, $${{t}_{R,}}$$  is given by:
 * $$R({{t}_{R}},V)={{e}^{-{{t}_{R}}\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}}}$$


 * $$\ln [R({{t}_{R}},V)]=-{{t}_{R}}\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}$$

or:
 * $${{t}_{R}}=-\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\ln [R({{t}_{R}},V)]$$