Template:MixedWeibullDistribution: Difference between revisions

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-=== The Mixed Weibull Distribution  ===
+#REDIRECT [[The_Mixed_Weibull_Distribution]]
-The mixed Weibull distribution is commonly used for modeling the behavior of components or systems exhibiting multiple failure modes (mixed populations). It gives the global picture of the life of a product by mixing different Weibull distributions for different stages of the product’s life and is defined by: <br>
-::<math>f_{S}(t)=\sum_{i=1}^{S}p_{i}\frac{\beta_{i}}{\eta_{i}}(\frac{t}{\eta_{i}})^{\beta_{i}-1}e^{-(\frac{t}{\eta_{i}})^{\beta_{i}}}
-</math>
-where the value of <span class="texhtml">''S''</span> is equal to the number of subpopulations. Note that this results in a total of <math>(3\cdot S-1)</math> parameters. In other words, each population has a portion or mixing weight for the <span class="texhtml">''i''<sup>''t''''h'''''h''</sup></span> population, a <span class="texhtml">β<sub>''i''</sub></span> , or shape parameter for the <span class="texhtml">''i''<sup>''t'''</sup></span> population and or scale parameter <span class="texhtml">η<sub>''i''</sub></span> for <span class="texhtml">''i''<sup>''t''''h'''</sup></span> population. Note that the parameters are reduced to <math>(3\cdot S-1)</math>, given the fact that the following condition can also be used: <br>
-::<math>\sum_{i=1}^{s}p_{i}=1</math>
-The mixed Weibull distribution and its characteristics are presented in detail in the chapter [[The Mixed Weibull Distribution]].