Template:Exponential Failure Rate Function: Difference between revisions
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(Created page with '===The Exponential Failure Rate Function=== The exponential failure rate function is: ::<math>\lambda (T)=\frac{f(T)}{R(T)}=\frac{\lambda {{e}^{-\lambda (T-\gamma )}}}{{{e}^{-\l…') |
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The exponential failure rate function is: | The exponential failure rate function is: | ||
::<math>\lambda ( | ::<math>\lambda (t)=\frac{f(t)}{R(t)}=\frac{\lambda {{e}^{-\lambda (t-\gamma )}}}{{{e}^{-\lambda (t-\gamma )}}}=\lambda =\text{constant}</math> | ||
Once again, note that the constant failure rate is a characteristic of the exponential distribution, and special cases of other distributions only. Most other distributions have failure rates that are functions of time. | Once again, note that the constant failure rate is a characteristic of the exponential distribution, and special cases of other distributions only. Most other distributions have failure rates that are functions of time. | ||
Revision as of 23:14, 7 February 2012
The Exponential Failure Rate Function
The exponential failure rate function is:
- [math]\displaystyle{ \lambda (t)=\frac{f(t)}{R(t)}=\frac{\lambda {{e}^{-\lambda (t-\gamma )}}}{{{e}^{-\lambda (t-\gamma )}}}=\lambda =\text{constant} }[/math]
Once again, note that the constant failure rate is a characteristic of the exponential distribution, and special cases of other distributions only. Most other distributions have failure rates that are functions of time.