Template:Aaw stat prob sum: Difference between revisions

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===Arrhenius-Weibull Statistical Properties Summary===
#REDIRECT [[Arrhenius_Relationship#Arrhenius-Weibull_Statistical_Properties_Summary]]
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{{aaw mean}}
 
{{aaw median}}
 
{{aaw mode}}
 
{{aaw sd}}
 
{{aaw rf}}
 
====Conditional Reliability Function====
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The Arrhenius-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( \tfrac{T+t}{\eta } \right)}^{\beta }}}}}{{{e}^{-{{\left( \tfrac{T}{\eta } \right)}^{\beta }}}}}</math>
 
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or:
 
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::<math>R(T,t,V)={{e}^{-\left[ {{\left( \tfrac{T+t}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta }}-{{\left( \tfrac{T}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta }} \right]}}</math>
 
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====Reliable Life====
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For the Arrhenius-Weibull relationship, 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}}=C\cdot {{e}^{\tfrac{B}{V}}}{{\left\{ -\ln \left[ R\left( {{t}_{R}},V \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>{\breve{T}</math>,
the median life, or the life by which half of the units will survive.
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====Arrhenius-Weibull Failure Rate Function====
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The Arrhenius-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)}=\frac{\beta }{C\cdot {{e}^{\tfrac{B}{V}}}}{{\left( \frac{T}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta -1}}</math>
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[[Image:ALTA6.9.gif|thumb|center|300px|Failure rate function for <math>\Beta<1 </math>, <math>\Beta=1 </math>, and <math>\Beta>1 </math>.]]
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Latest revision as of 04:38, 16 August 2012

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