Template:Alta exponential conditional reliability: Difference between revisions
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====Conditional Reliability==== | ==== Conditional Reliability ==== | ||
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: | ||
<br> | <br> | ||
::<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> | ||
<br> | <br> which says that the reliability for a mission of <span class="texhtml">''t''</span> duration, undertaken after the component or equipment has already accumulated <span class="texhtml">''T''</span> 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 | |||
<br> | <br> | ||
Revision as of 22:33, 6 March 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 t duration, undertaken after the component or equipment has already accumulated T 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."