Weibull++ Standard Folio Data 3 Subpop-Mixed Weibull: Difference between revisions

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#REDIRECT [[Weibull%2B%2B_Standard_Folio_Data_2_Subpop-Mixed_Weibull]]
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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.
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<math>{{f}_{1,...,S}(T)}</math> is given by<br>
<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 S=2, S=3, and S=4 for 2, 3 and 4 subpopulations respectively.
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| align="center" valign="middle" | [http://www.reliawiki.com/index.php/The_Mixed_Weibull_Distribution Get More Details...]
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| align="center" valign="middle" | [http://www.reliawiki.com/index.php/Weibull_Examples_Mixed See Examples...]
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Revision as of 18:24, 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 S=2, S=3, and S=4 for 2, 3 and 4 subpopulations respectively.

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