Estimating Fatigue Life of Structural Components from Accelerated Data via a Birnbaum-saunders Model with Shape and Scale Stress Dependent Parameters

The Birnbaum-Saunders model is widely applied to model fatigue failures caused by cyclic stresses both in the case of standard and accelerated life tests. This latter kind of tests are adopted when the product of interest is very reliable, in order to obtain failure data in a reasonably short amount of time. Estimates of the product's reliability or the long-term performances at normal use condition are then obtained, from accelerated failure data, adopting functional relationships accounting for the effect of the accelerating variables on the product's lifetime distribution. Customarily these models are formulated assuming that the accelerating variables affect the values of the lifetime distribution parameters, and not its form. In particular, in literature the Birnbaum-Saunders distribution is usually applied to accelerated data under the hypothesis that the scale parameter only depends on the stress conditions, while the shape parameter doesn't depend on them. In this paper, an applicative example is presented in which this standard model does not work satisfactorily. In fact, it is shown as, in the case of the considered real set of accelerated fatigue failure data, the Birnbaum-Saunders distribution, in which both scale and shape parameters depend on the stress conditions, fits the data significantly better than the abovementioned standard option. Difference among lifetime distribution estimates provided by the two different considered models are highlighted and discussed.