Template:Ipl ex rel function - Revision history

Richard House: Redirected page to Inverse Power Law (IPL) Relationship#IPL-Exponential

2012-08-15T23:09:37Z

Redirected page to Inverse Power Law (IPL) Relationship#IPL-Exponential

← Older revision		Revision as of 23:09, 15 August 2012
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	~~===IPL-Exponential Reliability Function===~~		#REDIRECT [[Inverse_Power_Law_(IPL)_Relationship#IPL-Exponential]]
	~~<br>~~
	~~The~~ IPL~~-exponential reliability function is given by:~~

	~~<br>~~
	~~::<math>R(T,V~~)~~={{e}^{-TK{{V}^{n}}}}</math>~~

	~~<br>~~
	~~This function is the complement of the~~ IPL-~~exponential cumulative distribution function:~~


	~~<br>~~
	~~::<math>R(T,V)=1-Q(T,V)=1-\int_{0}^{T}f(T,V)dT</math>~~

	~~<br>~~
	~~or:~~

	~~<br>~~
	~~::<math>R(T,V)=1-\int_{0}^{T}K{{V}^{n}}{{e}^{-K{{V}^{n}}T}}dT={{e}^{-K{{V}^{n}}T}}</math>~~

	~~<br>~~
	~~{{ipl ex conditional rel}}~~

	~~{{ipl ex reliable life}}~~

Athanasios Gerokostopoulos: /* IPL-Exponential Reliability Function */

2012-02-16T17:46:07Z

IPL-Exponential Reliability Function

← Older revision		Revision as of 17:46, 16 February 2012
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	<br>		<br>
	:or:		or:

	<br>		<br>

Athanasios Gerokostopoulos: /* IPL-Exponential Reliability Function */

2012-02-15T17:25:53Z

IPL-Exponential Reliability Function

← Older revision		Revision as of 17:25, 15 February 2012
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	<br>		<br>
	::<math>R(T,V)=1-Q(T,V)=1-\~~mathop{}_~~{0}^{T}f(T,V)dT</math>		::<math>R(T,V)=1-Q(T,V)=1-\int_{0}^{T}f(T,V)dT</math>

	<br>		<br>
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	<br>		<br>
	::<math>R(T,V)=1-\~~mathop{}_~~{0}^{T}K{{V}^{n}}{{e}^{-K{{V}^{n}}T}}dT={{e}^{-K{{V}^{n}}T}}</math>		::<math>R(T,V)=1-\int_{0}^{T}K{{V}^{n}}{{e}^{-K{{V}^{n}}T}}dT={{e}^{-K{{V}^{n}}T}}</math>

	<br>		<br>

Nicolette Young: /* Reliable Life */

2012-01-13T18:03:06Z

Reliable Life

← Older revision		Revision as of 18:03, 13 January 2012
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	{{ipl ex conditional rel}}		{{ipl ex conditional rel}}

	~~====Reliable Life====~~		{{ipl ex reliable life}}
	~~<br>~~
	~~For the IPL-exponential model, the~~ reliable life ~~or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is given by:~~

	~~<br>~~
	~~::<math>R({{t}_{R}},V)={{e}^{-K{{V}^{n}}{{t}_{R}}}}</math>~~

	~~<br>~~
	~~::<math>\ln [R({{t}_{R}},V)]=-K{{V}^{n}}{{t}_{R}}</math>~~

	~~<br>~~
	~~:or:~~

	~~<br>~~
	~~::<math>{{t}_{R}}=-\frac{1}{K{{V}^{n}}}\ln [R({{t}_{R~~}}~~,V)]</math>~~

	~~<br>~~

Nicolette Young: /* Conditional Reliability */

2012-01-13T18:02:38Z

Conditional Reliability

← Older revision		Revision as of 18:02, 13 January 2012
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	<br>		<br>
	~~====Conditional Reliability====~~		{{ipl ex conditional rel}}
	~~<br>~~
	~~The~~ conditional ~~reliability function for the IPL-exponential model is given by:~~

	~~<br>~~
	~~::<math>R(T,t,V)=\frac{R(T+t,V)}{R(T,V)}=\frac{{{e}^{-\lambda (T+t)}}}{{{e}^{-\lambda T}}}={{e}^{-K{{V}^{n}}t}}</math>~~

	~~<br>~~
	====Reliable Life====		====Reliable Life====
	<br>		<br>

Nicolette Young: Created page with '===IPL-Exponential Reliability Function===
The IPL-exponential reliability function is given by:
:: $R(T,V)={{e}^{-TK{{V}^{n}}}}$
This function is the …'

2012-01-13T17:59:35Z

Created page with '===IPL-Exponential Reliability Function=== The IPL-exponential reliability function is given by: ::<math>R(T,V)={{e}^{-TK{{V}^{n}}}}</math> This function is the …'

New page

===IPL-Exponential Reliability Function===
 
The IPL-exponential reliability function is given by:

 
::<math>R(T,V)={{e}^{-TK{{V}^{n}}}}</math>

 
This function is the complement of the IPL-exponential cumulative distribution function:

 
::<math>R(T,V)=1-Q(T,V)=1-\mathop{}_{0}^{T}f(T,V)dT</math>

 
:or:

 
::<math>R(T,V)=1-\mathop{}_{0}^{T}K{{V}^{n}}{{e}^{-K{{V}^{n}}T}}dT={{e}^{-K{{V}^{n}}T}}</math>

 
====Conditional Reliability====
 
The conditional reliability function for the IPL-exponential model is given by:

 
::<math>R(T,t,V)=\frac{R(T+t,V)}{R(T,V)}=\frac{{{e}^{-\lambda (T+t)}}}{{{e}^{-\lambda T}}}={{e}^{-K{{V}^{n}}t}}</math>

 
====Reliable Life====
 
For the IPL-exponential model, the reliable life or the mission duration for a desired reliability goal, <math>{{t}_{R}},</math> is given by:

 
::<math>R({{t}_{R}},V)={{e}^{-K{{V}^{n}}{{t}_{R}}}}</math>

 
::<math>\ln [R({{t}_{R}},V)]=-K{{V}^{n}}{{t}_{R}}</math>

 
:or:

 
::<math>{{t}_{R}}=-\frac{1}{K{{V}^{n}}}\ln [R({{t}_{R}},V)]</math>

Template:Ipl ex rel function - Revision history

Richard House: Redirected page to Inverse Power Law (IPL) Relationship#IPL-Exponential

Athanasios Gerokostopoulos: /* IPL-Exponential Reliability Function */

Athanasios Gerokostopoulos: /* IPL-Exponential Reliability Function */

Nicolette Young: /* Reliable Life */

Nicolette Young: /* Conditional Reliability */

Nicolette Young: Created page with '===IPL-Exponential Reliability Function=== The IPL-exponential reliability function is given by: ::R(T,V)={{e}^{-TK{{V}^{n}}}} This function is the …'

Nicolette Young: Created page with '===IPL-Exponential Reliability Function===
The IPL-exponential reliability function is given by:
:: $R(T,V)={{e}^{-TK{{V}^{n}}}}$
This function is the …'