Power-Law Accelerated Birnbaum–saunders Life Models

Abstract

An accelerated life testing procedure can reduce the lifetime of a material by observing the material's behavior under higher levels of stress than what is normally encountered. Useful inference hinges on the selection of an appropriate lifetime distribution and the substitution of an acceleration model for a distribution parameter, such as the mean or scale. The (inverse) power-law model is one such acceleration model that has applications to fatigue studies in metals, where failure tends to be crack-induced. The Birnbaum-Saunders distribution was developed to model fatigue in materials where the failure of a specimen is due to the propagation of a dominant crack. This paper will compare two Birnbaum-Saunders type models from the literature (that have power-law accelerated features) with a new but distinctive model proposed here. The new model is an accelerated life model for a reparameterization of the baseline distribution. Comparison of the three models will be via the aluminum coupon data set from Birnbaum and Saunders 5 and issues of accelerated testing will be discussed.