Estimating fatigue reliability of structural components via a Birnbaum-Saunders model with stress dependent parameters from accelerated life data

In this paper, the interest is in estimating the fatigue life distribution of highly reliable structural components from data obtained via accelerated life tests. These tests consist in subjecting the products of interest to stress levels more severe than those encountered in normal use. This forces the considered products to fail more quickly and allows collecting failure data in a reasonably short amount of time. Estimates of the product's reliability at normal use conditions are then extrapolated from accelerated failure data by adopting proper models. The model proposed in this paper generalizes a model which is widely applied in literature to analyze accelerated fatigue life data. In fact, as the abovementioned standard model it relies on two very classical assumptions, namely: a) the test conditions affect the lifetime distribution parameters, and not its form, and b) the fatigue life at each considered stress level follows a Birnbaum-Saunders distribution. On the other side, differently from the standard model, in which only the scale parameter depends on the stress conditions, the proposed model assumes that both the parameters of the Birnbaum-Saunders distribution possibly depend on the stress. The model is applied to a real set of accelerated fatigue failure data. Model parameters are estimated via the maximum likelihood method. The estimate of the reliability function at normal use conditions is extrapolated from the accelerated data. It is shown that the proposed Birnbaum-Saunders based model, in which both scale and shape parameters depend on the stress conditions, fits the considered data better than the model usually adopted in the literature. Differences among results provided by the two considered alternative models are highlighted and discussed. Finally two graphical strategies are proposed that allow judging the goodness of fit of the proposed model in absolute terms.