Template:Eyring-log rl - Revision history

Richard House: Redirected page to Eyring Relationship#Eyring-Lognormal

2012-08-16T23:40:24Z

Redirected page to Eyring Relationship#Eyring-Lognormal

← Older revision		Revision as of 23:40, 16 August 2012
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	~~====Reliable Life====~~		#REDIRECT [[Eyring_Relationship#Eyring-Lognormal]]
	~~<br>~~
	~~For the~~ Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is estimated by first solving the reliability equation with respect to time, as follows:

	~~<br>~~
	~~::<math>T_{R}^{\prime }=-\ln (V)-A+\frac{B}{V}+z\cdot {{\sigma }_{{{T}'}}}</math>~~

	~~<br>~~
	~~where:~~

	~~<br>~~
	~~::<math>z={{\Phi }^{-1}}\left[ F\left( T_{R}^{\prime },V \right) \right~~]~~</math>~~

	~~<br>~~
	~~and:~~

	~~<br>~~
	~~::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{z({T}',V)}{{e}^{-\tfrac{{{t}^{2}}}{2}}}dt</math>~~
	~~<br>~~
	~~<br>~~
	~~Since <math>{T}'=\ln (T)</math> the reliable life, <math>{{t}_{R,}}</math> is given by:~~

	~~<br>~~
	~~::<math>{{t}_{R}}={{e}^{T_{R}^{\prime }}}</math>~~

	~~<br>~~

Athanasios Gerokostopoulos: /* Reliable Life */

2012-02-27T23:54:01Z

Reliable Life

← Older revision		Revision as of 23:54, 27 February 2012
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	::<math>{{t}_{R}}={{e}^{T_{R}^{\prime }}}</math>		::<math>{{t}_{R}}={{e}^{T_{R}^{\prime }}}</math>

			<br>

Athanasios Gerokostopoulos: /* Reliable Life */

2012-02-14T23:14:02Z

Reliable Life

← Older revision		Revision as of 23:14, 14 February 2012
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	<br>		<br>
	::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\~~mathop{}_~~{-\infty }^{z({T}',V)}{{e}^{-\tfrac{{{t}^{2}}}{2}}}dt</math>		::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{z({T}',V)}{{e}^{-\tfrac{{{t}^{2}}}{2}}}dt</math>
	<br>		<br>
	<br>		<br>

Nicolette Young: Created page with '====Reliable Life====
For the Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, ${{t}_{R}},$ is estimated by fi…'

2012-01-12T23:05:49Z

Created page with '====Reliable Life==== For the Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is estimated by fi…'

New page

====Reliable Life====
 
For the Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is estimated by first solving the reliability equation with respect to time, as follows:

 
::<math>T_{R}^{\prime }=-\ln (V)-A+\frac{B}{V}+z\cdot {{\sigma }_{{{T}'}}}</math>

 
:where:

 
::<math>z={{\Phi }^{-1}}\left[ F\left( T_{R}^{\prime },V \right) \right]</math>

 
:and:

 
::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\mathop{}_{-\infty }^{z({T}',V)}{{e}^{-\tfrac{{{t}^{2}}}{2}}}dt</math>
 
 
Since <math>{T}'=\ln (T)</math> the reliable life, <math>{{t}_{R,}}</math> is given by:

 
::<math>{{t}_{R}}={{e}^{T_{R}^{\prime }}}</math>

Template:Eyring-log rl - Revision history

Richard House: Redirected page to Eyring Relationship#Eyring-Lognormal

Athanasios Gerokostopoulos: /* Reliable Life */

Athanasios Gerokostopoulos: /* Reliable Life */

Nicolette Young: Created page with '====Reliable Life==== For the Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, {{t}_{R}}, is estimated by fi…'

Nicolette Young: Created page with '====Reliable Life====
For the Eyring-lognormal model, the reliable life, or the mission duration for a desired reliability goal, ${{t}_{R}},$ is estimated by fi…'