Template:Bounds on Time FMB ED

Bounds on Time

The bounds around time for a given exponential percentile, or reliability value, are estimated by first solving the reliability equation with respect to time, or reliable life:

[math]\displaystyle{ \hat{t}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma } }[/math]

The corresponding confidence bounds are estimated from:

[math]\displaystyle{ \begin{align} & {{t}_{U}}= & -\frac{1}{{{\lambda }_{L}}}\cdot \ln (R)+\hat{\gamma } \\ & {{t}_{L}}= & -\frac{1}{{{\lambda }_{U}}}\cdot \ln (R)+\hat{\gamma } \end{align} }[/math]

The same equations apply for the one-parameter exponential with [math]\displaystyle{ \gamma =0. }[/math]