Template:Bounds on Reliability FMB ED: Difference between revisions
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(Created page with '====Bounds on Reliability==== The reliability of the two-parameter exponential distribution is: ::<math>\hat{R}(T;\hat{\lambda })={{e}^{-\hat{\lambda }(T-\hat{\gamma })}}</mat…') |
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::<math>\hat{R}( | ::<math>\hat{R}(t;\hat{\lambda })={{e}^{-\hat{\lambda }(t-\hat{\gamma })}}</math> | ||
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::<math>\begin{align} | ::<math>\begin{align} | ||
& {{R}_{L}}= & {{e}^{-{{\lambda }_{U}}( | & {{R}_{L}}= & {{e}^{-{{\lambda }_{U}}(t-\hat{\gamma })}} \\ | ||
& {{R}_{U}}= & {{e}^{-{{\lambda }_{L}}( | & {{R}_{U}}= & {{e}^{-{{\lambda }_{L}}(t-\hat{\gamma })}} | ||
\end{align}</math> | \end{align}</math> | ||
These equations hold true for the one-parameter exponential distribution, with <math>\gamma =0</math>. | These equations hold true for the one-parameter exponential distribution, with <math>\gamma =0</math>. | ||
Revision as of 23:50, 7 February 2012
Bounds on Reliability
The reliability of the two-parameter exponential distribution is:
- [math]\displaystyle{ \hat{R}(t;\hat{\lambda })={{e}^{-\hat{\lambda }(t-\hat{\gamma })}} }[/math]
The corresponding confidence bounds are estimated from:
- [math]\displaystyle{ \begin{align} & {{R}_{L}}= & {{e}^{-{{\lambda }_{U}}(t-\hat{\gamma })}} \\ & {{R}_{U}}= & {{e}^{-{{\lambda }_{L}}(t-\hat{\gamma })}} \end{align} }[/math]
These equations hold true for the one-parameter exponential distribution, with [math]\displaystyle{ \gamma =0 }[/math].