Template:Aw statistical properties summary: Difference between revisions

Latest revision as of 01:44, 16 August 2012

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+#REDIRECT [[Distributions_Used_in_Accelerated_Testing#The_Weibull_Distribution]]
-===Statistical Properties Summary===
-{{aw mean}}
-{{aw median}}
-{{aw mode}}
-{{aw standard deviation}}
-{{aw cdf and rf}}
-{{aw crf}}
-====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:
-::<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>,
-the median life, or the life by which half of the units will survive.
-<br>
-====The Failure Rate Function====
-The 2-parameter Weibull failure rate function,<math>\lambda (T)</math> ,
-is given by:
-::<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>