Template:Bounds on Time FMB ED - Revision history

Lisa Hacker: Redirected page to The Exponential Distribution

2012-08-10T06:52:18Z

Redirected page to The Exponential Distribution

← Older revision		Revision as of 06:52, 10 August 2012
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	~~====Bounds on Time====~~		#REDIRECT [[The Exponential Distribution]]

	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>\hat{t}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma }</math>~~


	~~The corresponding confidence bounds are estimated from:~~


	~~::<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>~~


	~~The same equations apply for the one-parameter exponential with <math>\gamma =0.</math>~~

Harry Guo: /* Bounds on Time */

2012-02-07T23:50:41Z

Bounds on Time

← Older revision		Revision as of 23:50, 7 February 2012
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	::<math>\hat{T}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma }</math>		::<math>\hat{t}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma }</math>


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	::<math>\begin{align}		::<math>\begin{align}
	& {{T}_{U}}= & -\frac{1}{{{\lambda }_{L}}}\cdot \ln (R)+\hat{\gamma } \\		& {{t}_{U}}= & -\frac{1}{{{\lambda }_{L}}}\cdot \ln (R)+\hat{\gamma } \\
	& {{T}_{L}}= & -\frac{1}{{{\lambda }_{U}}}\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>

Nicolette Young: 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…'

2012-01-04T16:07:14Z

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…'

New page

====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>\hat{T}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma }</math>

The corresponding confidence bounds are estimated from:

::<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>

The same equations apply for the one-parameter exponential with <math>\gamma =0.</math>