Template:Alta exponential reliable life

Reliable Life

The reliable life, or the mission duration for a desired reliability goal, [math]\displaystyle{ {{t}_{R}} }[/math] , for the 1-parameter exponential distribution is given by:

[math]\displaystyle{ \begin{align} & R({{t}_{R}})= {{e}^{-\lambda {{t}_{R}}}} \\ & & \\ & \ln [R({{t}_{R}})]= -\lambda {{t}_{R}} \end{align} }[/math]

or:

[math]\displaystyle{ {{t}_{R}}=-\frac{\ln [R({{t}_{R}})]}{\lambda } }[/math]