Template:Mixed weibull equations: Difference between revisions

Latest 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.