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| | | #REDIRECT [[Distributions_Used_in_Accelerated_Testing#The_Weibull_Distribution]] |
| ===Statistical Properties Summary===
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| {{aw mean}}
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| {{aw median}}
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| {{aw mode}}
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| {{aw standard deviation}}
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| {{aw cdf and rf}}
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| {{aw crf}}
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| ====The Reliable Life====
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| 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:
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| ::<math>{{T}_{R}}=\eta \cdot {{\left\{ -\ln \left[ R\left( {{T}_{R}} \right) \right] \right\}}^{\tfrac{1}{\beta }}}</math>
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| 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>,
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| the median life, or the life by which half of the units will survive.
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| <br>
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| ====The Failure Rate Function====
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| The 2-parameter Weibull failure rate function,<math>\lambda (T)</math> ,
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| is given by:
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| ::<math>\lambda \left( T \right)=\frac{f\left( T \right)}{R\left( T \right)}=\frac{\beta }{\eta }{{\left( \frac{T}{\eta } \right)}^{\beta -1}}</math>
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