  In this work, we present a statistical treatment of stress-life (S-N) data
drawn from a collection of records of fatigue experiments that were performed
on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of
materials by providing a systematic approach to model calibration, model
selection and model ranking with reference to S-N data. To this purpose, we
consider fatigue-limit models and random fatigue-limit models that are
specially designed to allow the treatment of the run-outs (right-censored
data). We first fit the models to the data by maximum likelihood methods and
estimate the quantiles of the life distribution of the alloy specimen. To
assess the robustness of the estimation of the quantile functions, we obtain
bootstrap confidence bands by stratified resampling with respect to the cycle
ratio. We then compare and rank the models by classical measures of fit based
on information criteria. We also consider a Bayesian approach that provides,
under the prior distribution of the model parameters selected by the user,
their simulation-based posterior distributions. We implement and apply Bayesian
model comparison methods, such as Bayes factor ranking and predictive
information criteria based on cross-validation techniques under various a
priori scenarios.
