Template:Exponential Reliable Life: Difference between revisions
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::<math>R({{t}_{R}})={{e}^{-\lambda ({{t}_{R}}-\gamma )}}</math> | ::<math>R({{t}_{R}})={{e}^{-\lambda ({{t}_{R}}-\gamma )}}</math> | ||
::<math>\ln [R({{t}_{R}})]=-\lambda ({{t}_{R}}-\gamma )</math> | ::<math>\ln[R({{t}_{R}})]=-\lambda({{t}_{R}}-\gamma )</math> | ||
or: | or: | ||
::<math>{{t}_{R}}=\gamma -\frac{\ln [R({{t}_{R}})]}{\lambda }</math> | ::<math>{{t}_{R}}=\gamma -\frac{\ln [R({{t}_{R}})]}{\lambda }</math> | ||
Revision as of 22:59, 7 February 2012
The Exponential Reliable Life
The reliable life, or the mission duration for a desired reliability goal, [math]\displaystyle{ {{t}_{R}} }[/math], for the one-parameter exponential distribution is:
- [math]\displaystyle{ R({{t}_{R}})={{e}^{-\lambda ({{t}_{R}}-\gamma )}} }[/math]
- [math]\displaystyle{ \ln[R({{t}_{R}})]=-\lambda({{t}_{R}}-\gamma ) }[/math]
or:
- [math]\displaystyle{ {{t}_{R}}=\gamma -\frac{\ln [R({{t}_{R}})]}{\lambda } }[/math]