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Selecting an Extreme-Value Distribution and the Transforming to a Specified Distribution

If a component fails when its weakest element fails, the component failure time will be the minimum of the failure times for its elements. Because the extreme value distributions are the possible limiting distributions for minimums, they become prime candidates for the failure time distribution. We provide a statistical methodology for selecting the best fitting distribution from among the three types of extreme value distributions. Our Bayesian approach is based on a three-parameter family of transformations that transforms the extreme value distributions to the standard exponential distribution.