Weibull++ Standard Folio Data 4 Subpop-Mixed Weibull: Difference between revisions

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====The Mixed Weibull Equations====
===4 Subpop Mixed Weibull===
Depending on the number of subpopulations chosen, Weibull++ uses the following equations for the reliability and probability density functions:
Mixed Weibull analysis is a method that can be used in situations when there are multiple failure behaviors, or trends, that exist in a single data set. The mixed Weibull method fits a single distribution with Weibull parameters and portion values for each subpopulation in the data set. The mixed Weibull distribution is also known as multi-modal Weibull.
 
 
<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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Revision as of 22:05, 29 February 2012

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4 Subpop Mixed Weibull

Mixed Weibull analysis is a method that can be used in situations when there are multiple failure behaviors, or trends, that exist in a single data set. The mixed Weibull method fits a single distribution with Weibull parameters and portion values for each subpopulation in the data set. The mixed Weibull distribution is also known as multi-modal Weibull.


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