Weibull++ Standard Folio Data 1P-Weibull: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
No edit summary
Line 10: Line 10:




The one-parameter Weibull distribution is a special case of obtained by setting
The one-parameter Weibull distribution is a special case of the two parameter Weibull that assumes that
::<math>\gamma=0 \,\!</math>
and assuming
::<math>\beta=C=Constant \,\!</math>  
::<math>\beta=C=Constant \,\!</math>  
or
 
::<math> f(t)={ \frac{C}{\eta }}\left( {\frac{t}{\eta }}\right) ^{C-1}e^{-\left( {\frac{t}{ \eta }}\right) ^{C}} \,\!</math>  
<math> f(t)={ \frac{C}{\eta }}\left( {\frac{t}{\eta }}\right) ^{C-1}e^{-\left( {\frac{t}{ \eta }}\right) ^{C}} \,\!</math>  


where the only unknown parameter is the scale parameter, <math>\eta\,\!</math>.  
where the only unknown parameter is the scale parameter, <math>\eta\,\!</math>.  

Revision as of 23:23, 10 February 2012

 

Webnotesbar.png

The One-Parameter Weibull Distribution

The one-parameter Weibull distribution is a special case of the two parameter Weibull that assumes that

[math]\displaystyle{ \beta=C=Constant \,\! }[/math]

or

[math]\displaystyle{ f(t)={ \frac{C}{\eta }}\left( {\frac{t}{\eta }}\right) ^{C-1}e^{-\left( {\frac{t}{ \eta }}\right) ^{C}} \,\! }[/math]

where the only unknown parameter is the scale parameter, [math]\displaystyle{ \eta\,\! }[/math].

Note that in the formulation of the one-parameter Weibull, we assume that the shape parameter [math]\displaystyle{ \beta \,\! }[/math] is known a priori from past experience on identical or similar products. The advantage of doing this is that data sets with few or no failures can be analyzed.


The Weibull Distribution
See an Example...


Docedit.png