Weibull++ Standard Folio Data 3P-Weibull: Difference between revisions

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<br><math> f(T)={ \frac{\beta }{\eta }}\left( {\frac{T-\gamma}{\eta }}\right) ^{\beta -1}e^{-\left( { \frac{T-\gamma}{\eta }}\right) ^{\beta }} \,\!</math>
<br><math> f(T)={ \frac{\beta }{\eta }}\left( {\frac{T-\gamma}{\eta }}\right) ^{\beta -1}e^{-\left( { \frac{T-\gamma}{\eta }}\right) ^{\beta }} \,\!</math>
<br>Beta is the shape parameter or slope. Values less than one incicate a decreasing failure rate, greater then one an increasing failure rate, and when one a constant failure rate. Eta is the scale parameter, or characteristic life.  Eta represents the time by which 63.2% of the units fail.
<br>Beta is the shape parameter or slope. Values less than one incicate a decreasing failure rate, greater then one an increasing failure rate, and when one a constant failure rate. Eta is the scale parameter, or characteristic life.  Eta represents the time by which 63.2% of the units fail.
Gamma is the location parameter that determines the starting location of the distribution. If gamma is positive it implies that no failutes can occur until time gamma is reached.<br>  
Gamma is the location parameter that determines the starting location of the distribution. If gamma is positive it implies that no failutes can occur until time gamma is reached. <br>  
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| align="center" valign="middle" | [http://www.reliawiki.com/index.php/The_Weibull_Distribution Get More Details...]
| align="center" valign="middle" | [http://www.reliawiki.com/index.php/The_Weibull_Distribution Get More Details...]
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| align="center" valign="middle" | [http://www.reliawiki.com/index.php/Weibull_Examples_2P See Examples...]
| align="center" valign="middle" | [http://www.reliawiki.com/index.php/Weibull_Examples_3P See Examples...]
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Revision as of 17:56, 11 November 2011

Reliability Web Notes

Weibull Folio
Life Data Analysis

The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering. It can model an increasing, decreasing and or constant failure rate behavior. The 3-parameter Weibull includes a location parameter gamma. It's pdf is given by:


[math]\displaystyle{ f(T)={ \frac{\beta }{\eta }}\left( {\frac{T-\gamma}{\eta }}\right) ^{\beta -1}e^{-\left( { \frac{T-\gamma}{\eta }}\right) ^{\beta }} \,\! }[/math]
Beta is the shape parameter or slope. Values less than one incicate a decreasing failure rate, greater then one an increasing failure rate, and when one a constant failure rate. Eta is the scale parameter, or characteristic life. Eta represents the time by which 63.2% of the units fail. Gamma is the location parameter that determines the starting location of the distribution. If gamma is positive it implies that no failutes can occur until time gamma is reached.

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