Weibull++ Standard Folio Data 2 Subpop-Mixed Weibull: Difference between revisions

Revision as of 18:18, 11 November 2011

Reliability Web Notes
Weibull Folio
Life Data Analysis
The mixed Weibull distribution (also known as a multimodal Weibull) is used to model data that do not fall on a straight line on a Weibull probability plot. Data of this type, particularly if the data points follow an S-shape on the probability plot, may be indicative of more than one failure mode at work in the population of failure times.
[math]\displaystyle{ {{f}_{1,...,S}(T)} }[/math] is given by [math]\displaystyle{ \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.
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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>
+<math>\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.