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

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==== The One-Parameter Weibull Distribution ====
==== The One-Parameter Weibull Distribution ====


The one-parameter Weibull is a special case of the Weibull distribution. function is obtained by again setting  
 
The one-parameter Weibull ''pdf'' is obtained by again setting  
<math>\gamma=0 \,\!</math> and assuming <math>\beta=C=Constant \,\!</math> assumed value or:  
<math>\gamma=0 \,\!</math> and assuming <math>\beta=C=Constant \,\!</math> assumed value or:  


[[Image:weibullreliabilityfunction.gif]]
<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 23:19, 10 February 2012

 

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The One-Parameter Weibull Distribution

The one-parameter Weibull pdf is obtained by again setting [math]\displaystyle{ \gamma=0 \,\! }[/math] and assuming [math]\displaystyle{ \beta=C=Constant \,\! }[/math] assumed value 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...


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