Template:One-parameter weibull distribution: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
Line 8: Line 8:
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 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.
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 with identical or similar products. The advantage of doing this is that data sets with few or no failures can be analyzed.

Revision as of 22:46, 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 with identical or similar products. The advantage of doing this is that data sets with few or no failures can be analyzed.