Template:Alta exponential reliability function: Difference between revisions
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====The Reliability Function==== | ==== The Reliability Function ==== | ||
The 1-parameter exponential reliability function is given by: | |||
The 1-parameter exponential reliability function is given by: | |||
<br> | |||
::<math>R(T)={{e}^{-\lambda T}}={{e}^{-\tfrac{T}{m}}}</math> | ::<math>R(T)={{e}^{-\lambda T}}={{e}^{-\tfrac{T}{m}}}</math> | ||
<br> | <br> This function is the complement of the exponential cumulative distribution function, or: | ||
This function is the complement of the exponential cumulative distribution function or: | |||
<br> | |||
::<math>R(T)=1-Q(T)=1-\int_{0}^{T}f(T)dT</math> | ::<math>R(T)=1-Q(T)=1-\int_{0}^{T}f(T)dT</math> | ||
<br> | <br> and: | ||
and: | |||
<br> | |||
::<math>R(T)=1-\int_{0}^{T}\lambda {{e}^{-\lambda T}}dT={{e}^{-\lambda T}}</math> | ::<math>R(T)=1-\int_{0}^{T}\lambda {{e}^{-\lambda T}}dT={{e}^{-\lambda T}}</math> | ||
<br> | <br> | ||
Revision as of 22:32, 6 March 2012
The Reliability Function
The 1-parameter exponential reliability function is given by:
- [math]\displaystyle{ R(T)={{e}^{-\lambda T}}={{e}^{-\tfrac{T}{m}}} }[/math]
This function is the complement of the exponential cumulative distribution function, or:
- [math]\displaystyle{ R(T)=1-Q(T)=1-\int_{0}^{T}f(T)dT }[/math]
and:
- [math]\displaystyle{ R(T)=1-\int_{0}^{T}\lambda {{e}^{-\lambda T}}dT={{e}^{-\lambda T}} }[/math]