Template:One-parameter weibull distribution: Difference between revisions
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==== The | ==== The 1-Parameter Weibull Distribution ==== | ||
The | The 1-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: | ||
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where the only unknown parameter is the scale parameter, <math>\eta\,\!</math>. | where the only unknown parameter is the scale parameter, <math>\eta\,\!</math>. | ||
Note that in the formulation of the | Note that in the formulation of the 1-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. | ||
Revision as of 22:41, 24 April 2012
The 1-Parameter Weibull Distribution
The 1-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 1-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.