Reliability statistical analysis about products of Birnbaum–Saunders fatigue life distribution for life test and progressive stress accelerated life test

Birnbaum–Saunders fatigue life distribution is an important failure model in the probability physical methods. It is more suitable for describing the life rules of fatigue failure products than common life distributions such as Weibull distribution and lognormal distribution. Besides, it is mainly applied to analytical research about fatigue failure and degradation failure of electronic product performance. The characteristic properties such as numerical characteristics and image features of density function and failure rate function are studied for generalized BS fatigue life distribution GBS(α, β, m) in this paper. Then the point estimates and approximate interval estimates of parameters are proposed for generalized BS fatigue life distribution GBS(α, β, m), and the precision of estimates are investigated by Monte Carlo simulations. Finally, when the scale parameter satisfies inverse power law model, the failure distribution model is given for the products of two-parameter BS fatigue life distribution BS(α, β) under progressive stress accelerated life test according to the time conversion idea of famous Nelson assumption, and then the points estimates of parameters are given.