Template:Eyring-ex rl

Reliable Life

For the Eyring-exponential model, the reliable life, or the mission duration for a desired reliability goal, [math]\displaystyle{ {{t}_{R,}} }[/math] is given by:

[math]\displaystyle{ R({{t}_{R}},V)={{e}^{-{{t}_{R}}\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}}} }[/math]

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

or:

[math]\displaystyle{ {{t}_{R}}=-\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\ln [R({{t}_{R}},V)] }[/math]