Template:Weibull Probability Density Function - Revision history

Richard House: Redirected page to The Weibull Distribution

2012-08-13T01:27:56Z

Redirected page to The Weibull Distribution

← Older revision		Revision as of 01:27, 13 August 2012
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	~~== Weibull Probability Density Function ==~~		#REDIRECT [[The Weibull Distribution]]

	~~====~~The ~~3-Parameter~~ Weibull Distribution~~====~~
	~~{{three-parameter weibull distribution}}~~

	~~{{Two-parameter weibull distribution}}~~

	~~{{one-parameter weibull distribution}}~~

Chris Kahn: /* Weibull Probability Density Function */

2012-04-24T22:44:26Z

Weibull Probability Density Function

← Older revision		Revision as of 22:44, 24 April 2012
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	== Weibull Probability Density Function ==		== Weibull Probability Density Function ==

	====The 3-Parameter Weibull Distribution		====The 3-Parameter Weibull Distribution====
	{{three-parameter weibull distribution}}		{{three-parameter weibull distribution}}

Chris Kahn: /* Weibull Probability Density Function */

2012-04-24T22:44:15Z

Weibull Probability Density Function

← Older revision		Revision as of 22:44, 24 April 2012
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	== Weibull Probability Density Function ==		== Weibull Probability Density Function ==

			====The 3-Parameter Weibull Distribution
	{{three-parameter weibull distribution}}		{{three-parameter weibull distribution}}

Nicolette Young: /* The One-Parameter Weibull Distribution */

2012-01-24T16:06:17Z

The One-Parameter Weibull Distribution

← Older revision		Revision as of 16:06, 24 January 2012
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	{{Two-parameter weibull distribution}}		{{Two-parameter weibull distribution}}

	~~=== The One-Parameter Weibull Distribution ===~~		{{one-parameter weibull distribution}}

	~~The~~ one-parameter ~~Weibull ''pdf'' is obtained by again setting~~
	~~<math>\gamma=0 \,\!</math> and assuming <math>\beta=C=Constant \,\!</math> assumed value or:~~

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

	~~where the only unknown parameter is the scale parameter, <math>\eta\,\!</math>.~~

	Note that in the formulation of the one-parameter Weibull, we assume that the shape parameter <math>\beta \,\!</math> is known ''a priori'' from past experience on identical or similar products. The advantage of doing this is that data sets with few or no failures can be analyzed.

Nicolette Young: /* The Two-Parameter Weibull Distribution */

2012-01-17T23:12:52Z

The Two-Parameter Weibull Distribution

← Older revision		Revision as of 23:12, 17 January 2012
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	{{three-parameter weibull distribution}}		{{three-parameter weibull distribution}}

	~~=== The~~ Two~~-Parameter Weibull Distribution ===~~		{{Two-parameter weibull distribution}}

	~~The two~~-parameter ~~Weibull ''pdf'' is obtained by setting~~
	~~<math> \gamma=0 \,\!</math>, and is given by:~~

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

	=== The One-Parameter Weibull Distribution ===		=== The One-Parameter Weibull Distribution ===

Nicolette Young: /* The Three-Parameter Weibull Distribution */

2012-01-17T23:09:04Z

The Three-Parameter Weibull Distribution

@@ Line 1: / Line 1: @@
 == Weibull Probability Density Function ==
-=== The Three-Parameter Weibull Distribution ===
+{{three-parameter weibull distribution}}
 === The Two-Parameter Weibull Distribution ===

Nicolette Young: Created page with '== Weibull Probability Density Function == === The Three-Parameter Weibull Distribution === The three-parameter Weibull ''pdf'' is given by: :: $f(T)={ \frac{\beta }{\et…'$

2012-01-04T16:27:25Z

Created page with '== Weibull Probability Density Function == === The Three-Parameter Weibull Distribution === The three-parameter Weibull ''pdf'' is given by: ::<math> f(T)={ \frac{\beta }{\et…'

New page

== Weibull Probability Density Function ==

=== The Three-Parameter Weibull Distribution ===

The three-parameter Weibull ''pdf'' is given by:

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

:where,

::<math> f(T)\geq 0,\text{ }T\geq 0\text{ or }\gamma, </math>

::<math>\beta>0\ \,\!</math>,

::<math> \eta > 0 \,\!</math>,

::<math> -\infty < \gamma < +\infty \,\!</math>

:and,

::<math> \eta= \,\!</math> scale parameter, or characteristic life
::<math> \beta= \,\!</math> shape parameter (or slope),
::<math> \gamma= \,\!</math> location parameter (or failure free life).

=== The Two-Parameter Weibull Distribution ===

The two-parameter Weibull ''pdf'' is obtained by setting
<math> \gamma=0 \,\!</math>, and is given by:

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

=== The One-Parameter Weibull Distribution ===

The one-parameter Weibull ''pdf'' is obtained by again setting
<math>\gamma=0 \,\!</math> and assuming <math>\beta=C=Constant \,\!</math> assumed value or:

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

where the only unknown parameter is the scale parameter, <math>\eta\,\!</math>.

Note that in the formulation of the one-parameter Weibull, we assume that the shape parameter <math>\beta \,\!</math> is known ''a priori'' from past experience on identical or similar products. The advantage of doing this is that data sets with few or no failures can be analyzed.

Template:Weibull Probability Density Function - Revision history

Richard House: Redirected page to The Weibull Distribution

Chris Kahn: /* Weibull Probability Density Function */

Chris Kahn: /* Weibull Probability Density Function */

Nicolette Young: /* The One-Parameter Weibull Distribution */

Nicolette Young: /* The Two-Parameter Weibull Distribution */

Nicolette Young: /* The Three-Parameter Weibull Distribution */

Nicolette Young: Created page with '== Weibull Probability Density Function == === The Three-Parameter Weibull Distribution === The three-parameter Weibull ''pdf'' is given by: :: f(T)={ \frac{\beta }{\et…'

Nicolette Young: Created page with '== Weibull Probability Density Function == === The Three-Parameter Weibull Distribution === The three-parameter Weibull ''pdf'' is given by: :: $f(T)={ \frac{\beta }{\et…'$