Template:Alta exponential distribution - Revision history

Richard House: Redirected page to Distributions Used in Accelerated Testing

2012-08-16T01:08:31Z

Redirected page to Distributions Used in Accelerated Testing

← Older revision		Revision as of 01:08, 16 August 2012
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	~~== The Exponential Distribution ==~~		#REDIRECT [[Distributions_Used_in_Accelerated_Testing]]

	The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by:

	~~<br>~~

	~~::<math>\begin{align}~~
	~~& f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\~~
	~~& T\ge 0,\lambda >0,m>0~~
	~~\end{align}</math>~~

	~~<br> where:~~

	~~::*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement (e.g. failures per hour, per cycle, etc.).~~
	~~::*<math>\lambda =\tfrac{1}{m}</math>.~~
	~~::*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.~~
	::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.

Richard House at 01:08, 16 August 2012

2012-08-16T01:08:00Z

← Older revision		Revision as of 01:08, 16 August 2012
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	::*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.		::*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.
	::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.		::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.

	~~{{alta statistical properties summary}}~~

Richard House at 01:04, 16 August 2012

2012-08-16T01:04:14Z

← Older revision		Revision as of 01:04, 16 August 2012
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	::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.		::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.

	{{alta statistical properties summary}}		{{alta statistical properties summary}}

	~~{{characteristics of the exponential distribution alta~~}}

Chris Kahn at 22:35, 6 March 2012

2012-03-06T22:35:13Z

← Older revision		Revision as of 22:35, 6 March 2012
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	== The Exponential Distribution ==		== The Exponential Distribution ==

	The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by:		The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by:

	<br>		<br>

	::<math>\begin{align}		::<math>\begin{align}
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	\end{align}</math>		\end{align}</math>

	<br>		<br> where:
	where:

	::*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement (e.g. failures per hour, per cycle, etc.).		::*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement (e.g. failures per hour, per cycle, etc.).

Chris Kahn at 22:34, 6 March 2012

2012-03-06T22:34:25Z

← Older revision		Revision as of 22:34, 6 March 2012
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	== The Exponential Distribution ==		== The Exponential Distribution ==

	The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by: <br>		The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by:

			<br>

	::<math>\begin{align}		::<math>\begin{align}
	& f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\		& f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\
	& T\ge 0,\lambda >0,m>0		& T\ge 0,\lambda >0,m>0
	\end{align}</math~~><br~~>		\end{align}</math>

			<br>
	where:		where:

Chris Kahn at 22:29, 6 March 2012

2012-03-06T22:29:36Z

← Older revision		Revision as of 22:29, 6 March 2012
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	where:		where:

	::*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement, e.g. failures per hour, per cycle, etc.		::*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement (e.g. failures per hour, per cycle, etc.).
	::*<math>\lambda =\tfrac{1}{m}.</math>		::*<math>\lambda =\tfrac{1}{m}</math>.
	::*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.		::*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.
	::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.		::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.

Chris Kahn at 22:28, 6 March 2012

2012-03-06T22:28:24Z

← Older revision		Revision as of 22:28, 6 March 2012
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	== The Exponential Distribution ==		== The Exponential Distribution ==

	The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases ~~to which~~ it ~~does not~~ apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by: <br>		The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by: <br>

	::<math>\begin{align}		::<math>\begin{align}

Chris Kahn at 22:27, 6 March 2012

2012-03-06T22:27:38Z

Chris Kahn at 22:26, 6 March 2012

2012-03-06T22:26:24Z

← Older revision		Revision as of 22:26, 6 March 2012
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	==The Exponential Distribution==		== The Exponential Distribution ==
	~~<br>~~

	The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate.		The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by:
	The single-parameter exponential ~~<math>~~pdf~~</math>~~ is given by:

			:<math>\begin{align}
	::<math>\begin{align}
	& f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\		& f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\
	& T\ge 0,\lambda >0,m>0		& T\ge 0,\lambda >0,m>0
	\end{align}</math>		\end{align}</math>

			where:

	~~where~~:		:*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement, e.g. failures per hour, per cycle, etc.
	~~::•~~ <~~math~~>~~\lambda~~ =</~~math~~> constant failure rate, in failures per unit of measurement, e.g. failures per hour, per cycle, etc.		:*<math>\lambda =\tfrac{1}{m}.</math>
	::• <math>\lambda =\tfrac{1}{m}.</math>		:*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.
	::• <~~math~~>m=</~~math~~> mean time between failures, or to a failure.		:*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.
	::• <~~math~~>T=</~~math~~> operating time, life, or age, in hours, cycles, miles, actuations, etc.


	This distribution requires the estimation of only one parameter, <~~math~~>~~\lambda~~ </~~math~~> , for its application.

	~~<br>~~		{{alta statistical properties summary}}
	{{alta statistical properties summary}}

	{{characteristics of the exponential distribution alta}}		{{characteristics of the exponential distribution alta}}

Athanasios Gerokostopoulos: /* The Exponential Distribution */

2012-02-27T23:20:40Z

The Exponential Distribution

← Older revision		Revision as of 23:20, 27 February 2012
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	The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate.		The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate.
	The single-parameter exponential <math>pdf</math> is given by:		The single-parameter exponential <math>pdf</math> is given by:
	~~<br>~~

	::<math>\begin{align}		::<math>\begin{align}
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	& T\ge 0,\lambda >0,m>0		& T\ge 0,\lambda >0,m>0
	\end{align}</math>		\end{align}</math>
	~~<br>~~

	:where:
			where:
	::• <math>\lambda =</math> constant failure rate, in failures per unit of measurement, e.g. failures per hour, per cycle, etc.		::• <math>\lambda =</math> constant failure rate, in failures per unit of measurement, e.g. failures per hour, per cycle, etc.
	::• <math>\lambda =\tfrac{1}{m}.</math>		::• <math>\lambda =\tfrac{1}{m}.</math>
	::• <math>m=</math> mean time between failures, or to a failure.		::• <math>m=</math> mean time between failures, or to a failure.
	::• <math>T=</math> operating time, life, or age, in hours, cycles, miles, actuations, etc.		::• <math>T=</math> operating time, life, or age, in hours, cycles, miles, actuations, etc.
	~~<br>~~

	This distribution requires the estimation of only one parameter, <math>\lambda </math> , for its application.		This distribution requires the estimation of only one parameter, <math>\lambda </math> , for its application.

	<br>		<br>
	{{alta statistical properties summary}}		{{alta statistical properties summary}}

	{{characteristics of the exponential distribution alta}}		{{characteristics of the exponential distribution alta}}

← Older revision		Revision as of 22:27, 6 March 2012
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	== The Exponential Distribution ==		== The Exponential Distribution ==

	The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by:		The exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate. The single-parameter exponential ''pdf ''is given by: <br>

	:<math>\begin{align}		::<math>\begin{align}
	& f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\		& f(T)= \lambda {{e}^{-\lambda T}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}T}} \\
	& T\ge 0,\lambda >0,m>0		& T\ge 0,\lambda >0,m>0
	\end{align}</math>		\end{align}</math><br>

	where:		where:

	:*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement, e.g. failures per hour, per cycle, etc.		::*<span class="texhtml">λ = </span> constant failure rate, in failures per unit of measurement, e.g. failures per hour, per cycle, etc.
	:*<math>\lambda =\tfrac{1}{m}.</math>		::*<math>\lambda =\tfrac{1}{m}.</math>
	:*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.		::*<span class="texhtml">''m'' = </span> mean time between failures, or to a failure.
	:*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.		::*<span class="texhtml">''T'' = </span> operating time, life, or age, in hours, cycles, miles, actuations, etc. This distribution requires the estimation of only one parameter, <span class="texhtml">λ</span> , for its application.

	{{alta statistical properties summary}}		{{alta statistical properties summary}}

	{{characteristics of the exponential distribution alta}}		{{characteristics of the exponential distribution alta}}