Template:Mixed weibull regression solution - Revision history

Richard House: Redirected page to The Mixed Weibull Distribution#Mixed Weibull Parameter Estimation

2012-08-15T00:38:17Z

Redirected page to The Mixed Weibull Distribution#Mixed Weibull Parameter Estimation

← Older revision		Revision as of 00:38, 15 August 2012
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	~~'''Regression Solution'''~~		#REDIRECT [[The_Mixed_Weibull_Distribution#Mixed_Weibull_Parameter_Estimation]]

	Weibull++ utilizes a modified Levenberg-Marquardt algorithm (non-linear regression) when performing regression analysis on a mixed Weibull distribution. The procedure is rather involved and is beyond the scope of this reference. It is sufficient to say that the algorithm fits a curved line of the form:

	~~::<math>{{R}_{1,...,S}}(t)=\underset{i=1}{\overset{S}{\mathop \sum }}\,{{\rho }_{i}}\cdot {{e}^{-{{\left( \tfrac{t}{{{\eta }_{i}}} \right)}^{{{\beta }_{i}}}}}}</math>~~
	~~where:~~

	~~::<math>\underset{i=1}{\overset{S}{\mathop \sum }}\,{{\rho }_{i}}=1</math>~~

	to the parameters <math>\widehat{{{\rho }_{1,\text{ }}}}</math> <math>\widehat{{{\beta }_{1}}},</math> <math>\widehat{{{\eta }_{1}}},</math> <math>\widehat{{{\rho }_{2,\text{ }}}}\widehat{{{\beta }_{2}}},</math> <math>\widehat{{{\eta }_{2}}},...,</math> <math>\widehat{{{\rho }_{S,}}\text{ }}\widehat{{{\beta }_{S}}},</math> <math>\widehat{{{\eta }_{S}}},</math> utilizing the times-to-failure and their respective plotting positions. It is important to note that in the case of regression analysis, using a mixed Weibull model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.

Harry Guo at 18:12, 14 February 2012

2012-02-14T18:12:56Z

← Older revision		Revision as of 18:12, 14 February 2012
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	Weibull++ utilizes a modified Levenberg-Marquardt algorithm (non-linear regression) when performing regression analysis on a mixed Weibull distribution. The procedure is rather involved and is beyond the scope of this reference. It is sufficient to say that the algorithm fits a curved line of the form:		Weibull++ utilizes a modified Levenberg-Marquardt algorithm (non-linear regression) when performing regression analysis on a mixed Weibull distribution. The procedure is rather involved and is beyond the scope of this reference. It is sufficient to say that the algorithm fits a curved line of the form:

	::<math>{{R}_{1,...,S}}(T)=\underset{i=1}{\overset{S}{\mathop \sum }}\,{{\rho }_{i}}\cdot {{e}^{-{{\left( \tfrac{T}{{{\eta }_{i}}} \right)}^{{{\beta }_{i}}}}}}</math>		::<math>{{R}_{1,...,S}}(t)=\underset{i=1}{\overset{S}{\mathop \sum }}\,{{\rho }_{i}}\cdot {{e}^{-{{\left( \tfrac{t}{{{\eta }_{i}}} \right)}^{{{\beta }_{i}}}}}}</math>
	:where:		where:

	::<math>\underset{i=1}{\overset{S}{\mathop \sum }}\,{{\rho }_{i}}=1</math>		::<math>\underset{i=1}{\overset{S}{\mathop \sum }}\,{{\rho }_{i}}=1</math>

	to the parameters <math>\widehat{{{\rho }_{1,\text{ }}}}</math> <math>\widehat{{{\beta }_{1}}},</math> <math>\widehat{{{\eta }_{1}}},</math> <math>\widehat{{{\rho }_{2,\text{ }}}}\widehat{{{\beta }_{2}}},</math> <math>\widehat{{{\eta }_{2}}},...,</math> <math>\widehat{{{\rho }_{S,}}\text{ }}\widehat{{{\beta }_{S}}},</math> <math>\widehat{{{\eta }_{S}}},</math> utilizing the times-to-failure and their respective plotting positions. It is important to note that in the case of regression analysis, using a mixed Weibull model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.		to the parameters <math>\widehat{{{\rho }_{1,\text{ }}}}</math> <math>\widehat{{{\beta }_{1}}},</math> <math>\widehat{{{\eta }_{1}}},</math> <math>\widehat{{{\rho }_{2,\text{ }}}}\widehat{{{\beta }_{2}}},</math> <math>\widehat{{{\eta }_{2}}},...,</math> <math>\widehat{{{\rho }_{S,}}\text{ }}\widehat{{{\beta }_{S}}},</math> <math>\widehat{{{\eta }_{S}}},</math> utilizing the times-to-failure and their respective plotting positions. It is important to note that in the case of regression analysis, using a mixed Weibull model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.

Harry Guo at 17:26, 14 February 2012

2012-02-14T17:26:44Z

← Older revision		Revision as of 17:26, 14 February 2012
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	~~====~~Regression Solution~~====~~		'''Regression Solution'''

	Weibull++ utilizes a modified Levenberg-Marquardt algorithm (non-linear regression) when performing regression analysis on a mixed Weibull distribution. The procedure is rather involved and is beyond the scope of this reference. It is sufficient to say that the algorithm fits a curved line of the form:		Weibull++ utilizes a modified Levenberg-Marquardt algorithm (non-linear regression) when performing regression analysis on a mixed Weibull distribution. The procedure is rather involved and is beyond the scope of this reference. It is sufficient to say that the algorithm fits a curved line of the form:

Nicolette Young: Created page with '====Regression Solution==== Weibull++ utilizes a modified Levenberg-Marquardt algorithm (non-linear regression) when performing regression analysis on a mixed Weibull distributio…'

2012-01-04T18:41:07Z

Created page with '====Regression Solution==== Weibull++ utilizes a modified Levenberg-Marquardt algorithm (non-linear regression) when performing regression analysis on a mixed Weibull distributio…'

New page

====Regression Solution====
Weibull++ utilizes a modified Levenberg-Marquardt algorithm (non-linear regression) when performing regression analysis on a mixed Weibull distribution. The procedure is rather involved and is beyond the scope of this reference. It is sufficient to say that the algorithm fits a curved line of the form:

::<math>{{R}_{1,...,S}}(T)=\underset{i=1}{\overset{S}{\mathop \sum }}\,{{\rho }_{i}}\cdot {{e}^{-{{\left( \tfrac{T}{{{\eta }_{i}}} \right)}^{{{\beta }_{i}}}}}}</math>
:where:

::<math>\underset{i=1}{\overset{S}{\mathop \sum }}\,{{\rho }_{i}}=1</math>

to the parameters <math>\widehat{{{\rho }_{1,\text{ }}}}</math> <math>\widehat{{{\beta }_{1}}},</math> <math>\widehat{{{\eta }_{1}}},</math> <math>\widehat{{{\rho }_{2,\text{ }}}}\widehat{{{\beta }_{2}}},</math> <math>\widehat{{{\eta }_{2}}},...,</math> <math>\widehat{{{\rho }_{S,}}\text{ }}\widehat{{{\beta }_{S}}},</math> <math>\widehat{{{\eta }_{S}}},</math> utilizing the times-to-failure and their respective plotting positions. It is important to note that in the case of regression analysis, using a mixed Weibull model, the choice of regression axis, i.e. <math>RRX</math> or <math>RRY,</math> is of no consequence since non-linear regression is utilized.