Template:Ipl ex rel function: Difference between revisions

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(Created page with '===IPL-Exponential Reliability Function=== <br> The IPL-exponential reliability function is given by: <br> ::<math>R(T,V)={{e}^{-TK{{V}^{n}}}}</math> <br> This function is the …')
 
 
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===IPL-Exponential Reliability Function===
#REDIRECT [[Inverse_Power_Law_(IPL)_Relationship#IPL-Exponential]]
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The IPL-exponential reliability function is given by:
 
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::<math>R(T,V)={{e}^{-TK{{V}^{n}}}}</math>
 
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This function is the complement of the IPL-exponential cumulative distribution function:
 
 
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::<math>R(T,V)=1-Q(T,V)=1-\mathop{}_{0}^{T}f(T,V)dT</math>
 
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:or:
 
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::<math>R(T,V)=1-\mathop{}_{0}^{T}K{{V}^{n}}{{e}^{-K{{V}^{n}}T}}dT={{e}^{-K{{V}^{n}}T}}</math>
 
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====Conditional Reliability====
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The conditional reliability function for the IPL-exponential model is given by:
 
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::<math>R(T,t,V)=\frac{R(T+t,V)}{R(T,V)}=\frac{{{e}^{-\lambda (T+t)}}}{{{e}^{-\lambda T}}}={{e}^{-K{{V}^{n}}t}}</math>
 
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====Reliable Life====
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For the IPL-exponential model, the reliable life or the mission duration for a desired reliability goal,  <math>{{t}_{R}},</math>  is given by:
 
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::<math>R({{t}_{R}},V)={{e}^{-K{{V}^{n}}{{t}_{R}}}}</math>
 
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::<math>\ln [R({{t}_{R}},V)]=-K{{V}^{n}}{{t}_{R}}</math>
 
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:or:
 
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::<math>{{t}_{R}}=-\frac{1}{K{{V}^{n}}}\ln [R({{t}_{R}},V)]</math>
 
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Latest revision as of 23:09, 15 August 2012

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