The ββ-Birnbaum–Saunders distribution: An improved distribution for fatigue life modeling

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies. For the first time, based on this distribution, the so-called ββ-Birnbaum–Saunders distribution is proposed for fatigue life modeling. Various properties of the new model including expansions for the moments, moment generating function, mean deviations, density function of the order statistics and their moments are derived. We discuss maximum likelihood estimation of the model’s parameters. The superiority of the new model is illustrated by means of three failure real data sets.