Weibull++ Standard Folio Data 3 Subpop-Mixed Weibull: Difference between revisions
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{{ | ====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. | |||
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| valign="middle" | [http://www.reliawiki.com/index.php/The_Mixed_Weibull_Distribution The Mixed Weibull Distribution] | | valign="middle" | [http://www.reliawiki.com/index.php/The_Mixed_Weibull_Distribution The Mixed Weibull Distribution] |
Revision as of 22:54, 7 February 2012
The Mixed Weibull EquationsDepending on the number of subpopulations chosen, Weibull++ uses the following equations for the reliability and probability density functions:
and: [math]\displaystyle{ {{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]\displaystyle{ S=2 }[/math] , [math]\displaystyle{ S=3 }[/math] , and [math]\displaystyle{ 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. |
The Mixed Weibull Distribution |