Template:Eyring-weibull stat prop sum: Difference between revisions

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===Eyring-Weibull Statistical Properties Summary===
#REDIRECT [[Eyring_Relationship#Eyring-Weibull]]
 
{{eyring-weib mean}}
 
{{eyring-weib median}}
 
{{eyring-weib mode}}
 
{{eyring-weib sd}}
 
{{eyring-weib rf}}
 
====Conditional Reliability Function====
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The Eyring-Weibull conditional reliability function at a specified stress level is given by:
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::<math>R(T,t,V)=\frac{R(T+t,V)}{R(T,V)}=\frac{{{e}^{-{{\left( \left( T+t \right)\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta }}}}}{{{e}^{-{{\left( V\cdot T\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta }}}}}</math>
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:or:
 
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::<math>R(T,t,V)={{e}^{-\left[ {{\left( \left( T+t \right)\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta }}-{{\left( V\cdot T\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta }} \right]}}</math>
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====Reliable Life====
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For the Eyring-Weibull model, the reliable life,  <math>{{t}_{R}}</math> , of a unit for a specified reliability and starting the mission at age zero is given by:
 
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::<math>{{t}_{R}}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}{{\left\{ -\ln \left[ R\left( {{T}_{R}},V \right) \right] \right\}}^{\tfrac{1}{\beta }}}</math>
 
 
====Eyring-Weibull Failure Rate Function====
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The Eyring-Weibull failure rate function,  <math>\lambda (T)</math> , is given by:
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::<math>\lambda \left( T,V \right)=\frac{f\left( T,V \right)}{R\left( T,V \right)}=\beta {{\left( T\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta -1}}</math>
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Latest revision as of 23:14, 16 August 2012

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