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The Weibull Analysis Handbook, Second Edition by Bryan Dodson. ASQ Quality Press, Milwaukee, Wisconsin, 2006. xiv+184 pp. $90.00 (Nonmember).
IT IS WELL KNOWN that the Weibull distribution is named after Waloddi Weibull, the Swedish physicist, who used it to model the distribution of breaking strengths of materials [Weibull (1939a,b)]. It was twelve years later that Weibull (1951) demonstrated that the Weibull distribution would be a good model in modeling data from many other applications by showing that it provides a very close approximation to observed data. The observed data he used for this purpose were as diverse as yield strength of Bofors' steel, fatigue life of an ST-37 steel, length of syrtoideas, fiber strength of Indian cotton, stature of adult males born in the British Isles, and breadths of beans of Phaseolus vulgaris. However, what is probably not well known is that the Weibull distribution had been used, prior to Weibull, by Rosen and Rammler (1933) for describing the law governing the fineness of powdered coal.
The Weibull distribution, as established by Fréchet (1927), Fisher and Tippett (1928) and Gnedenko (1943), is one of three extreme value distributions corresponding to the limiting distribution of the sample maxima. For this reason, the Weibull distribution also goes sometimes under the names Fréchet distribution, Weibull-Gnedenko distribution, and extreme value distribution.
The Weibull distribution is simply a power transformation of the exponential distribution, and it possesses considerable flexibility as it has increasing failure rate (IFR) when the shape parameter β is more than 1, constant failure rate (Exponential) when β equals 1,...