A Bayesian analysis of fatigue data

Abstract: The aim of the present paper is to bring arguments in favour of Bayesian inference in the context of fatigue testing. In fact, life tests play a central role in the design of mechanical systems, as their structural reliability depends in part on the fatigue strength of material, which need to be determined by experiments. The classical statistical analysis, however, can lead to results of limited practical usefulness when the number of specimens on test is small. Instead, despite the little attention paid to it in this context, Bayes approach can potentially give more accurate estimates by combining test data with technological knowledge available from theoretical studies and/or previous experimental results, thus contributing to save time and money. Hence, for the case of steel alloys, a discussion about the usually available technological knowledge is presented and methods to properly formalize it in the form of prior credibility density functions are proposed. Further, the performances of the proposed Bayesian procedures are analysed on the basis of simulation studies, showing that they can largely outperform the conventional ones at the expense of a moderate increase of the computational effort