Lifetime distribution selection for complete and censored multi-level testing data and its influence on probability of failure estimates

A general method of lifetime distribution selection for multi-level complete and censored testing data is developed. To alleviate the scarcity of test samples at each individual stress levels, a mathematical model is incorporated to correlate the lifetimes and stresses allowing for utilizing the multi-level lifetime data as a whole. Probabilistic modeling of the model prediction error is made and the equivalence between the lifetime distribution and the error distribution is shown. Based on the error modeling and likelihood functions, a Bayesian framework for lifetime distribution selection is proposed. It is shown that the classical information criterion is a local measure and the Bayes factor is a global measure over the likelihood space. A two-step assessment procedure integrating the goodness-of-fit and asymptotic Bayes factors is given. The proposed method is demonstrated using three engineering examples. Comparisons between the proposed method and the conventional methods such as ratio test and the difference of information criteria are made. The influence of the distribution selection on the subsequent probability of failure estimates is discussed.