Bayesian methods for a growth-curve degradation model with repeated measures

The increasing reliability of some manufactured products has led to fewer observed failures in reliability testing. Thus, useful inference on the distribution of failure times is often not possible using traditional survival analysis methods. Partly as a result of this difficulty, there has been increasing interest in inference from degradation measurements made on products prior to failure. In the degradation literature inference is commonly based on large-sample theory and, if the degradation path model is nonlinear, their implementation can be complicated by the need for approximations. In this paper we review existing methods and then describe a fully Bayesian approach which allows approximation-free inference. We focus on predicting the failure time distribution of both future units and those that are currently under test. The methods are illustrated using fatigue crack growth data.