Template:Mixed weibull equations - Revision history

Richard House: Redirected page to The Mixed Weibull Distribution#The Mixed Weibull Equations

2012-08-15T00:35:12Z

Redirected page to The Mixed Weibull Distribution#The Mixed Weibull Equations

← Older revision		Revision as of 00:35, 15 August 2012
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	~~===The Mixed Weibull Equations===~~		#REDIRECT [[The_Mixed_Weibull_Distribution#The_Mixed_Weibull_Equations]]
	~~Depending on the number of subpopulations chosen, Weibull++ uses the following equations for the reliability and probability density functions:~~


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

	~~and:~~

	::<math>{{f}_{1,...,S}}(t)=\underset{i=1}{\overset{S}{\mathop \sum }}\,\frac{{{N}_{i}}{{\beta }_{i}}}{N{{\eta }_{i}}}{{\left( \frac{t}{{{\eta }_{i}}} \right)}^{{{\beta }_{i}}-1}}{{e}^{-{{(\tfrac{t}{{{\eta }_{i}}})}^{{{\beta }_{i}}}}}}</math>

	where <math>S=2</math> , <math>S=3</math> , and <math>S=4</math> for 2, 3 and 4 subpopulations respectively. Weibull++ uses a non-linear regression method or direct maximum likelihood methods to estimate the parameters.

Harry Guo: /* The Mixed Weibull Equations */

2012-02-14T18:01:12Z

The Mixed Weibull Equations

← Older revision		Revision as of 18:01, 14 February 2012
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	::<math>{{R}_{1,...,S}}(T)=\underset{i=1}{\overset{S}{\mathop \sum }}\,\frac{{{N}_{i}}}{N}{{e}^{-{{\left( \tfrac{T}{{{\eta }_{i}}} \right)}^{{{\beta }_{i}}}}}}</math>		::<math>{{R}_{1,...,S}}(t)=\underset{i=1}{\overset{S}{\mathop \sum }}\,\frac{{{N}_{i}}}{N}{{e}^{-{{\left( \tfrac{t}{{{\eta }_{i}}} \right)}^{{{\beta }_{i}}}}}}</math>

	:and:		and:

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

	where <math>S=2</math> , <math>S=3</math> , and <math>S=4</math> for 2, 3 and 4 subpopulations respectively. Weibull++ uses a non-linear regression method or direct maximum likelihood methods to estimate the parameters.		where <math>S=2</math> , <math>S=3</math> , and <math>S=4</math> for 2, 3 and 4 subpopulations respectively. Weibull++ uses a non-linear regression method or direct maximum likelihood methods to estimate the parameters.

Harry Guo: /* The Mixed Weibull Equations */

2012-02-14T17:23:59Z

The Mixed Weibull Equations

← Older revision		Revision as of 17:23, 14 February 2012
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	====The Mixed Weibull Equations====		===The Mixed Weibull Equations===
	Depending on the number of subpopulations chosen, Weibull++ uses the following equations for the reliability and probability density functions:		Depending on the number of subpopulations chosen, Weibull++ uses the following equations for the reliability and probability density functions:

Nicolette Young: Created page with '====The Mixed Weibull Equations==== Depending on the number of subpopulations chosen, Weibull++ uses the following equations for the reliability and probability density functions…'

2012-01-24T16:32:42Z

Created page with '====The Mixed Weibull Equations==== Depending on the number of subpopulations chosen, Weibull++ uses the following equations for the reliability and probability density functions…'

New page

====The Mixed Weibull Equations====
Depending on the number of subpopulations chosen, Weibull++ uses the following equations for the reliability and probability density functions:

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

:and:

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

where <math>S=2</math> , <math>S=3</math> , and <math>S=4</math> for 2, 3 and 4 subpopulations respectively. Weibull++ uses a non-linear regression method or direct maximum likelihood methods to estimate the parameters.