On the Relationship between Two Fatigue-Life Models

The relationship between two fatigue life distributions, namely the Birnbaum-Saunders and the Inverse Gaussian, is further investigated. An intimate connection exists between the two models, viz, the Birnbaum-Saunders is a mixture of two probability distributions: 1) an Inverse Gaussian random variable, and 2) the reciprocal of an Inverse Gaussian random variable. Advantages and disadvantages of the two distributions are discussed. The arguments favour the Birnbaum-Saunders distribution from a stochastic modeling point of view, whereas the Inverse Gaussian distribution seems to be the more attractive of the two with respect to statistical analysis and analysis of censored data.