Weibull Probability Density Function

The Three-Parameter Weibull Distribution

The three-parameter Weibull pdf is given by:

where,

and,

η = scale parameter,
β = shape parameter (or slope),
γ = location parameter.

The Two-Parameter Weibull Distribution

The two-parameter Weibull pdf is obtained by setting γ = 0 and is given by:

(1)

The One-Parameter Weibull Distribution

The one-parameter Weibull pdf is obtained by again setting γ = 0 and assuming β = C = constant = assumed value or:

(2)

where the only unknown parameter is the scale parameter, η. Note that in the formulation of the one-parameter Weibull, we assume that the shape parameter β 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.