A Birnbaum-Saunders accelerated life model

The 2-parameter family of probability distributions introduced by Birnbaum & Saunders characterizes the fatigue failure of materials subjected to cyclic stresses and strains. It is shown that the methods of accelerated life testing are applicable to the Birnbaum–Saunders distribution for analyzing accelerated lifetime data, and the (inverse) power law model is used due to its justification for describing accelerated fatigue failure in metals. This paper develops the (inverse) power law accelerated form of the Birnbaum–Saunders distribution, and explores the corresponding inference procedures—including parameter estimation techniques and the derivation of the -expected Fisher information matrix. The model approach in this paper is different from an earlier work, which considered a log-linear form of a model with applications to accelerated life testing. Here, using an example data set, the fitted model is effectively used to estimate lower distribution percentiles and mean failure times for particular values of the acceleration variable. The benefits of having an operable closed form of the Fisher information matrix, which is unique to this article for this model, include interval estimation of model parameters and LCB on percentiles using relatively simple computational procedures.