Template:Exponential Reliability Function: Difference between revisions
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(Created page with '===The Exponential Reliability Function=== The equation for the two-parameter exponential cumulative density function, or <math>cdf,</math> is given by: ::<math>F(T)=Q(T)=1-{{e…') |
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::<math>F( | ::<math>F(t)=Q(t)=1-{{e}^{-\lambda (t-\gamma )}}</math> | ||
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::<math>R( | ::<math>R(t)=1-Q(t)=1-\int_{0}^{t-\gamma }f(x)dx</math> | ||
::<math>R( | ::<math>R(t)=1-\int_{0}^{t-\gamma }\lambda {{e}^{-\lambda x}}dx={{e}^{-\lambda (t-\gamma )}}</math> | ||
Revision as of 23:13, 7 February 2012
The Exponential Reliability Function
The equation for the two-parameter exponential cumulative density function, or [math]\displaystyle{ cdf, }[/math] is given by:
- [math]\displaystyle{ F(t)=Q(t)=1-{{e}^{-\lambda (t-\gamma )}} }[/math]
Recalling that the reliability function of a distribution is simply one minus the [math]\displaystyle{ cdf }[/math], the reliability function of the two-parameter exponential distribution is given by:
- [math]\displaystyle{ R(t)=1-Q(t)=1-\int_{0}^{t-\gamma }f(x)dx }[/math]
- [math]\displaystyle{ R(t)=1-\int_{0}^{t-\gamma }\lambda {{e}^{-\lambda x}}dx={{e}^{-\lambda (t-\gamma )}} }[/math]