Template:Bounds on Reliability FMB ED

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].