Template:Alta exponential conditional reliability: Difference between revisions
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(Created page with '====Conditional Reliability==== <br> The conditional reliability function for the 1-parameter exponential distribution is given by: <br> ::<math>R(T,t)=\frac{R(T+t)}{R(T)}=\frac…') |
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The conditional reliability function for the 1-parameter exponential distribution is given by: | The conditional reliability function for the 1-parameter exponential distribution is given by: | ||
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::<math>R(T,t)=\frac{R(T+t)}{R(T)}=\frac{{{e}^{-\lambda (T+t)}}}{{{e}^{-\lambda T}}}={{e}^{-\lambda t}}</math> | ::<math>R(T,t)=\frac{R(T+t)}{R(T)}=\frac{{{e}^{-\lambda (T+t)}}}{{{e}^{-\lambda T}}}={{e}^{-\lambda t}}</math> | ||
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which says that the reliability for a mission of <math>t</math> duration undertaken after the component or equipment has already accumulated <math>T</math> hours of operation from age zero is only a function of the mission duration, and not a function of the age at the beginning of the mission. This is referred to as the ``memoryless property.'' | which says that the reliability for a mission of <math>t</math> duration undertaken after the component or equipment has already accumulated <math>T</math> hours of operation from age zero is only a function of the mission duration, and not a function of the age at the beginning of the mission. This is referred to as the ``memoryless property.'' | ||
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Revision as of 23:22, 27 February 2012
Conditional Reliability
The conditional reliability function for the 1-parameter exponential distribution is given by:
- [math]\displaystyle{ R(T,t)=\frac{R(T+t)}{R(T)}=\frac{{{e}^{-\lambda (T+t)}}}{{{e}^{-\lambda T}}}={{e}^{-\lambda t}} }[/math]
which says that the reliability for a mission of [math]\displaystyle{ t }[/math] duration undertaken after the component or equipment has already accumulated [math]\displaystyle{ T }[/math] hours of operation from age zero is only a function of the mission duration, and not a function of the age at the beginning of the mission. This is referred to as the ``memoryless property.