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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:
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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>
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| :and:
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| ::<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>
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| 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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