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(Created page with '====The Reliable Life==== For the 2-parameter Weibull distribution, the reliable life, <math>{{T}_{R}}</math> , of a unit for a specified reliability, starting the mission at ag…') |
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====The Reliable Life==== | ====The Reliable Life==== | ||
For the 2-parameter Weibull distribution, the reliable life, <math>{{T}_{R}}</math> , of a unit for a specified reliability, starting the mission at age zero, is given by: | For the 2-parameter Weibull distribution, the reliable life, <math>{{T}_{R}}</math> , of a unit for a specified reliability, starting the mission at age zero, is given by: | ||
::<math>{{T}_{R}}=\eta \cdot {{\left\{ -\ln \left[ R\left( {{T}_{R}} \right) \right] \right\}}^{\tfrac{1}{\beta }}}</math> | ::<math>{{T}_{R}}=\eta \cdot {{\left\{ -\ln \left[ R\left( {{T}_{R}} \right) \right] \right\}}^{\tfrac{1}{\beta }}}</math> | ||
This is the life for which the unit will function successfully with a reliability of <math>R({{T}_{R}})</math> . If <math>R({{T}_{R}})=0.50</math> then <math>{{T}_{R}}=\breve{T}</math>, | This is the life for which the unit will function successfully with a reliability of <math>R({{T}_{R}})</math> . If <math>R({{T}_{R}})=0.50</math> then <math>{{T}_{R}}=\breve{T}</math>, | ||
the median life, or the life by which half of the units will survive. | the median life, or the life by which half of the units will survive. | ||
<br> | <br> | ||
Revision as of 22:34, 27 February 2012
The Reliable Life
For the 2-parameter Weibull distribution, the reliable life, [math]\displaystyle{ {{T}_{R}} }[/math] , of a unit for a specified reliability, starting the mission at age zero, is given by:
- [math]\displaystyle{ {{T}_{R}}=\eta \cdot {{\left\{ -\ln \left[ R\left( {{T}_{R}} \right) \right] \right\}}^{\tfrac{1}{\beta }}} }[/math]
This is the life for which the unit will function successfully with a reliability of [math]\displaystyle{ R({{T}_{R}}) }[/math] . If [math]\displaystyle{ R({{T}_{R}})=0.50 }[/math] then [math]\displaystyle{ {{T}_{R}}=\breve{T} }[/math],
the median life, or the life by which half of the units will survive.