Template:Weibull mean - Revision history

Richard House: Redirected page to Weibull Distribution Functions

2012-08-13T01:39:29Z

Redirected page to Weibull Distribution Functions

← Older revision		Revision as of 01:39, 13 August 2012
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	~~=== The Mean or MTTF ===~~		#REDIRECT [[Weibull Distribution Functions]]

	~~The mean, <math> \overline{T} \,\!</math>, (also called ''MTTF'' of the~~ Weibull ~~''pdf'' is given by:~~

	~~::<math> \overline{T}=\gamma +\eta \cdot \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>~~

	~~where~~
	~~::<math> \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>~~

	~~is the gamma function evaluated at the value of~~

	~~::<math> \left( { \frac{1}{\beta }}+1\right) \,\!</math>.~~

	~~The gamma function is defined as:~~

	~~::<math> \Gamma (n)=\int_{0}^{\infty }e^{-x}x^{n-1}dx \,\!</math>~~

	~~For the 2-parameter case, this can be reduced to:~~

	~~::<math> \overline{T}=\eta \cdot \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>~~

	~~Note that some practitioners erroneously assume that <math> \eta \,\!</math> is equal to the MTTF, <math> \overline{T}\,\!</math>.~~
	~~This is only true for the case of~~
	~~<math> \beta=1 \,\!</math> or~~

	~~::<math>~~
	~~\begin{align}~~
	~~\overline{T} &= \eta \cdot \Gamma \left( {\frac{1}{1}}+1\right) \\~~
	~~&= \eta \cdot \Gamma \left( {\frac{1}{1}}+1\right) \\~~
	~~&= \eta \cdot \Gamma \left( {2}\right) \\~~
	~~&= \eta \cdot 1\\~~
	~~&= \eta~~
	~~\end{align}~~
	~~</math>~~

Chris Kahn: /* The Mean or MTTF */

2012-04-24T22:52:40Z

The Mean or MTTF

← Older revision		Revision as of 22:52, 24 April 2012
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	::<math> \Gamma (n)=\int_{0}^{\infty }e^{-x}x^{n-1}dx \,\!</math>		::<math> \Gamma (n)=\int_{0}^{\infty }e^{-x}x^{n-1}dx \,\!</math>

	For the ~~two~~-parameter case, this can be reduced to:		For the 2-parameter case, this can be reduced to:

	::<math> \overline{T}=\eta \cdot \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>		::<math> \overline{T}=\eta \cdot \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>

Harry Guo: /* The Mean or MTTF */

2012-02-09T21:29:34Z

The Mean or MTTF

← Older revision		Revision as of 21:29, 9 February 2012
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	::<math> \overline{T}=\gamma +\eta \cdot \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>		::<math> \overline{T}=\gamma +\eta \cdot \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>

	:where		where
	::<math> \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>		::<math> \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>

Nicolette Young: Created page with '=== The Mean or MTTF === The mean, $\overline{T} \,\!$ , (also called ''MTTF'' of the Weibull ''pdf'' is given by: :: $\overline{T}=\gamma +\eta \cdot \Gamma \…'$

2012-01-04T16:31:34Z

Created page with '=== The Mean or MTTF === The mean, <math> \overline{T} \,\!</math>, (also called ''MTTF'' of the Weibull ''pdf'' is given by: ::<math> \overline{T}=\gamma +\eta \cdot \Gamma \…'

New page

=== The Mean or MTTF ===

The mean, <math> \overline{T} \,\!</math>, (also called ''MTTF'' of the Weibull ''pdf'' is given by:

::<math> \overline{T}=\gamma +\eta \cdot \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>

:where
::<math> \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>

is the gamma function evaluated at the value of

::<math> \left( { \frac{1}{\beta }}+1\right) \,\!</math>.

The gamma function is defined as:

::<math> \Gamma (n)=\int_{0}^{\infty }e^{-x}x^{n-1}dx \,\!</math>

For the two-parameter case, this can be reduced to:

::<math> \overline{T}=\eta \cdot \Gamma \left( {\frac{1}{\beta }}+1\right) \,\!</math>

Note that some practitioners erroneously assume that <math> \eta \,\!</math> is equal to the MTTF, <math> \overline{T}\,\!</math>.
This is only true for the case of
<math> \beta=1 \,\!</math> or

::<math>
\begin{align}
\overline{T} &= \eta \cdot \Gamma \left( {\frac{1}{1}}+1\right) \\
&= \eta \cdot \Gamma \left( {\frac{1}{1}}+1\right) \\
&= \eta \cdot \Gamma \left( {2}\right) \\
&= \eta \cdot 1\\
&= \eta
\end{align}
</math>

Template:Weibull mean - Revision history

Richard House: Redirected page to Weibull Distribution Functions

Chris Kahn: /* The Mean or MTTF */

Harry Guo: /* The Mean or MTTF */

Nicolette Young: Created page with '=== The Mean or MTTF === The mean, \overline{T} \,\!, (also called ''MTTF'' of the Weibull ''pdf'' is given by: :: \overline{T}=\gamma +\eta \cdot \Gamma \…'

Nicolette Young: Created page with '=== The Mean or MTTF === The mean, $\overline{T} \,\!$ , (also called ''MTTF'' of the Weibull ''pdf'' is given by: :: $\overline{T}=\gamma +\eta \cdot \Gamma \…'$