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

Revision as of 16:03, 24 January 2012

Reliability Web Notes
Weibull Folio
Life Data Analysis
Three-Parameter Weibull Distribution
The 3-parameter Weibull 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] where: [math]\displaystyle{ f(t)\geq 0,\text{ }t\geq \gamma \,\! }[/math] [math]\displaystyle{ \beta\gt 0\ \,\! }[/math] [math]\displaystyle{ \eta \gt 0 \,\! }[/math] [math]\displaystyle{ -\infty \lt \gamma \lt +\infty \,\! }[/math] and: [math]\displaystyle{ \eta= \,\! }[/math] scale parameter, or characteristic life [math]\displaystyle{ \beta= \,\! }[/math] shape parameter (or slope) [math]\displaystyle{ \gamma= \,\! }[/math] location parameter (or failure free life)

The Weibull Distribution
See Examples...

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-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:
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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>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>
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 | align="center" valign="middle" | [http://www.reliawiki.com/index.php/The_Weibull_Distribution The Weibull Distribution]