Template:Alta al rl: Difference between revisions
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For the Arrhenius-lognormal model, the reliable life, or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is estimated by first solving the reliability equation with respect to time, as follows: | For the Arrhenius-lognormal model, the reliable life, or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is estimated by first solving the reliability equation with respect to time, as follows: | ||
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::<math>{{T}'_{R}}= ln(C)+\frac{B}{V}+z \cdot {{\sigma}_{{T}'}}</math> | ::<math>{{T}'_{R}}= ln(C)+\frac{B}{V}+z \cdot {{\sigma}_{{T}'}}</math> | ||
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::<math>{{t}_{R}}={{e}^{T_{R}^{\prime }}}</math> | ::<math>{{t}_{R}}={{e}^{T_{R}^{\prime }}}</math> | ||
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Revision as of 23:38, 27 February 2012
Reliable Life
For the Arrhenius-lognormal model, the reliable life, or the mission duration for a desired reliability goal, [math]\displaystyle{ {{t}_{R}}, }[/math] is estimated by first solving the reliability equation with respect to time, as follows:
- [math]\displaystyle{ {{T}'_{R}}= ln(C)+\frac{B}{V}+z \cdot {{\sigma}_{{T}'}} }[/math]
where:
- [math]\displaystyle{ z={{\Phi }^{-1}}\left[ F\left( T_{R}^{\prime },V \right) \right] }[/math]
and:
- [math]\displaystyle{ \Phi (z)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{z({T}',V)}{{e}^{-\tfrac{{{t}^{2}}}{2}}}dt }[/math]
Since [math]\displaystyle{ {T}'=\ln (T) }[/math] the reliable life, [math]\displaystyle{ {{t}_{R}}, }[/math] is given by:
- [math]\displaystyle{ {{t}_{R}}={{e}^{T_{R}^{\prime }}} }[/math]