Template:One-parameter weibull distribution: Difference between revisions

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Note that in the formulation of the one-parameter Weibull, we assume that the shape parameter <math>\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.
Note that in the formulation of the one-parameter Weibull, we assume that the shape parameter <math>\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.
[[Category:Needs an example]]

Revision as of 20:30, 7 February 2012

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.