Template:Ald rf - Revision history

Richard House: Redirected page to Distributions Used in Accelerated Testing#The Lognormal Distribution

2012-08-16T03:15:18Z

Redirected page to Distributions Used in Accelerated Testing#The Lognormal Distribution

← Older revision		Revision as of 03:15, 16 August 2012
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	~~====Reliability Function====~~		#REDIRECT [[Distributions_Used_in_Accelerated_Testing#The_Lognormal_Distribution]]
	~~For the lognormal distribution, the reliability for a mission of time <math>T</math>, starting at age 0, is given by:~~

	~~<br>~~
	~~::<math>R(T)=\int_{T}^{\infty }f(t)dt</math>~~

	~~or:~~

	~~::<math>R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math>~~
	~~<br>~~

	~~There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables.~~

	~~<br>~~

Chris Kahn: /* Reliability Function */

2012-03-07T16:55:33Z

Reliability Function

← Older revision		Revision as of 16:55, 7 March 2012
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	====Reliability Function====		====Reliability Function====
	For the lognormal distribution, the reliability for a mission of time <math>T</math> , starting at age 0, is given by:		For the lognormal distribution, the reliability for a mission of time <math>T</math>, starting at age 0, is given by:

	<br>		<br>
	::<math>R(T)=\int_{T}^{\infty }f(t)dt</math>		::<math>R(T)=\int_{T}^{\infty }f(t)dt</math>
	~~<br>~~
	or:		or:
	~~<br>~~
	::<math>R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math>		::<math>R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math>
	<br>		<br>

	There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables.		There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables.
	~~<br>~~
	<br>		<br>

Athanasios Gerokostopoulos: /* Reliability Function */

2012-02-27T23:29:43Z

Reliability Function

← Older revision		Revision as of 23:29, 27 February 2012
Line 1:		Line 1:
	====Reliability Function====		====Reliability Function====
	For the lognormal distribution, the reliability for a mission of time <math>T</math> , starting at age 0, is given by:		For the lognormal distribution, the reliability for a mission of time <math>T</math> , starting at age 0, is given by:

	<br>		<br>
	::<math>R(T)=\int_{T}^{\infty }f(t)dt</math>		::<math>R(T)=\int_{T}^{\infty }f(t)dt</math>
	<br>		<br>
	:or:		or:
	<br>		<br>
	::<math>R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math>		::<math>R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math>

Athanasios Gerokostopoulos: /* Reliability Function */

2012-02-07T00:50:01Z

Reliability Function

← Older revision		Revision as of 00:50, 7 February 2012
Line 2:		Line 2:
	For the lognormal distribution, the reliability for a mission of time <math>T</math> , starting at age 0, is given by:		For the lognormal distribution, the reliability for a mission of time <math>T</math> , starting at age 0, is given by:
	<br>		<br>
	::<math>R(T)=\~~mathop{}_~~{T}^{\infty }f(t)dt</math>		::<math>R(T)=\int_{T}^{\infty }f(t)dt</math>
	<br>		<br>
	:or:		:or:
	<br>		<br>
	::<math>R(T)=\~~mathop{}_~~{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math>		::<math>R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math>
	<br>		<br>
	There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables.		There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables.
	<br>		<br>
	<br>		<br>

Nicolette Young: Created page with '====Reliability Function==== For the lognormal distribution, the reliability for a mission of time $T$ , starting at age 0, is given by:
:: $R(T)=\mathop{}_{…'$

2012-01-12T18:51:32Z

Created page with '====Reliability Function==== For the lognormal distribution, the reliability for a mission of time <math>T</math> , starting at age 0, is given by: ::<math>R(T)=\mathop{}_{…'

New page

====Reliability Function====
For the lognormal distribution, the reliability for a mission of time <math>T</math> , starting at age 0, is given by:
 
::<math>R(T)=\mathop{}_{T}^{\infty }f(t)dt</math>
 
:or:
 
::<math>R(T)=\mathop{}_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math>
 
There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables.

Template:Ald rf - Revision history

Richard House: Redirected page to Distributions Used in Accelerated Testing#The Lognormal Distribution

Chris Kahn: /* Reliability Function */

Athanasios Gerokostopoulos: /* Reliability Function */

Athanasios Gerokostopoulos: /* Reliability Function */

Nicolette Young: Created page with '====Reliability Function==== For the lognormal distribution, the reliability for a mission of time T , starting at age 0, is given by: ::R(T)=\mathop{}_{…'

Nicolette Young: Created page with '====Reliability Function==== For the lognormal distribution, the reliability for a mission of time $T$ , starting at age 0, is given by:
:: $R(T)=\mathop{}_{…'$