Template:Weibull Distribution Definition - Revision history

Richard House at 18:22, 24 September 2012

2012-09-24T18:22:30Z

← Older revision		Revision as of 18:22, 24 September 2012
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	The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or systems. In its most general case, the 3-parameter Weibull ''pdf'' is defined by: <br>		The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or systems. In its most general case, the 3-parameter Weibull ''pdf'' is defined by: <br>

	::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>		::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}\,\!</math>

	where <math>\beta \,\!</math> = shape parameter, <math>\eta \,\!</math> = scale parameter and <math>\gamma\,\!</math> = location parameter.		where <math>\beta \,\!</math> = shape parameter, <math>\eta \,\!</math> = scale parameter and <math>\gamma\,\!</math> = location parameter.

	If the location parameter, <math>\gamma\,\!</math> , is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:		If the location parameter, <math>\gamma\,\!</math>, is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:

	::<math>f(t)=\frac{\beta}{\eta }( \frac{t }{\eta } )^{\beta -1}{e}^{-(\tfrac{t }{\eta }) ^{\beta}}</math>		::<math>f(t)=\frac{\beta}{\eta }( \frac{t }{\eta } )^{\beta -1}{e}^{-(\tfrac{t }{\eta }) ^{\beta}}\,\!</math>

	One additional form is the 1-parameter Weibull distribution, which assumes that the location parameter, <math>\gamma\,\!</math> is zero, and the shape parameter is a known constant, or <math>\beta \,\!</math> = constant = <math>C\,\!</math>, so:		One additional form is the 1-parameter Weibull distribution, which assumes that the location parameter, <math>\gamma\,\!</math> is zero, and the shape parameter is a known constant, or <math>\beta \,\!</math> = constant = <math>C\,\!</math>, so:

	::<math>f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}		::<math>f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}
	</math>		\,\!</math>

	For a detailed discussion of this distribution, see [[The Weibull Distribution]].		For a detailed discussion of this distribution, see [[The Weibull Distribution]].

Richard House at 20:26, 29 August 2012

2012-08-29T20:26:30Z

← Older revision		Revision as of 20:26, 29 August 2012
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	The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or systems. In its most general case, the 3-parameter Weibull ~~<math>~~pdf~~</math>~~ is defined by: <br>		The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or systems. In its most general case, the 3-parameter Weibull ''pdf'' is defined by: <br>

	::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>		::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>

Richard House at 00:34, 22 August 2012

2012-08-22T00:34:06Z

← Older revision		Revision as of 00:34, 22 August 2012
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	::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>		::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>

	where <~~span class="texhtml"~~>~~β =~~ </~~span~~>shape parameter, <~~span class="texhtml"~~>~~η =~~ </~~span~~>scale parameter and <~~span class="texhtml"~~>γ</~~span~~> = location parameter.		where <math>\beta \,\!</math> = shape parameter, <math>\eta \,\!</math> = scale parameter and <math>\gamma\,\!</math> = location parameter.

	If the location parameter, <~~span class="texhtml"~~>γ</~~span~~> , is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:		If the location parameter, <math>\gamma\,\!</math> , is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:

	::<math>f(t)=\frac{\beta}{\eta }( \frac{t }{\eta } )^{\beta -1}{e}^{-(\tfrac{t }{\eta }) ^{\beta}}</math>		::<math>f(t)=\frac{\beta}{\eta }( \frac{t }{\eta } )^{\beta -1}{e}^{-(\tfrac{t }{\eta }) ^{\beta}}</math>

	One additional form is the 1-parameter Weibull distribution, which assumes that the location parameter, <~~span class="texhtml"~~>γ,</~~span~~> is zero, and the shape parameter is a known constant, or <~~span class="texhtml"~~>~~β =~~ </~~span~~>constant <~~span class="texhtml"~~>~~= ''~~C''</~~span~~>, so:		One additional form is the 1-parameter Weibull distribution, which assumes that the location parameter, <math>\gamma\,\!</math> is zero, and the shape parameter is a known constant, or <math>\beta \,\!</math> = constant = <math>C\,\!</math>, so:

	::<math>f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}		::<math>f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}

Melinda Caroline at 03:08, 17 August 2012

2012-08-17T03:08:30Z

← Older revision		Revision as of 03:08, 17 August 2012
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	::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>		::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>

	where <span class="texhtml">β = </span>shape parameter, <span class="texhtml">η = </span>scale parameter and γ = location parameter.		where <span class="texhtml">β = </span>shape parameter, <span class="texhtml">η = </span>scale parameter and <span class="texhtml">γ</span> = location parameter.

	If the location parameter, <span class="texhtml">γ</span> , is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:		If the location parameter, <span class="texhtml">γ</span> , is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:

Richard House at 01:42, 8 August 2012

2012-08-08T01:42:25Z

← Older revision		Revision as of 01:42, 8 August 2012
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	::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>		::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>

	~~<br>~~		where <span class="texhtml">β = </span>shape parameter, <span class="texhtml">η = </span>scale parameter and γ = location parameter.

	where <span class="texhtml">β = </span>shape parameter, <span class="texhtml">η = </span>scale parameter and γ = location parameter. ~~<br>~~

	If the location parameter, <span class="texhtml">γ</span> , is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:		If the location parameter, <span class="texhtml">γ</span> , is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:

Lisa Hacker: Created page with 'The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or sys…'

2012-08-07T03:12:29Z

Created page with 'The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or sys…'

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The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or systems. In its most general case, the 3-parameter Weibull <math>pdf</math> is defined by: 

::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>

 

where β = shape parameter, η = scale parameter and γ = location parameter. 

If the location parameter, γ , is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:

::<math>f(t)=\frac{\beta}{\eta }( \frac{t }{\eta } )^{\beta -1}{e}^{-(\tfrac{t }{\eta }) ^{\beta}}</math>

One additional form is the 1-parameter Weibull distribution, which assumes that the location parameter, γ, is zero, and the shape parameter is a known constant, or β = constant = ''C'', so:

::<math>f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}
</math>

For a detailed discussion of this distribution, see [[The Weibull Distribution]].