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| == Weibull Statistical Properties ==
| | #REDIRECT [[Weibull Distribution Functions]] |
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| {{weibull mean}}
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| {{weibull median}}
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| {{weibull mode}}
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| {{weibull standard deviation}}
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| {{weibull reliability function}}
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| {{weibull conditional reliability function}}
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| === The Weibull Reliable Life ===
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| The reliable life, <math> T_{R} \,\!</math>, of a unit for a specified reliability,<math> R \,\!</math>, starting the mission at age zero, is given by:
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| ::<math> T_{R}=\gamma +\eta \cdot \left\{ -\ln ( R ) \right\} ^{ \frac{1}{\beta }} </math>
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| This is the life for which the unit/item will be functioning successfully with a reliability of <math> R \,\!</math>, . If ,<math> 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.
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| === The Weibull Failure Rate Function ===
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| The Weibull failure rate function, <math> \lambda(t) \,\!</math>, 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-\gamma }{\eta }\right) ^{\beta -1} </math>
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