The Weibull family of probability distributions ( see also Generalized Weibull Distributions) is one the most widely used parametric families of distributions for modeling failure times or lifetimes. This is especially true in engineering and science applications (as suggested originally by Weibull, 1951) and is mainly due to the variety of shapes of its density function and the behaviors of its failure rate function. Literally thousands of references to the Weibull distribution can be found in the scientific literature.