Template:Bounds on Time FMB ED: Difference between revisions
Jump to navigation
Jump to search
(Created page with '====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 t…') |
|||
| Line 4: | Line 4: | ||
::<math>\hat{ | ::<math>\hat{t}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma }</math> | ||
| Line 11: | Line 11: | ||
::<math>\begin{align} | ::<math>\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> | \end{align}</math> | ||
The same equations apply for the one-parameter exponential with <math>\gamma =0.</math> | The same equations apply for the one-parameter exponential with <math>\gamma =0.</math> | ||
Revision as of 23:50, 7 February 2012
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]