Advances in Bayesian decision making in reliability

Starting in the late 80s Bayesian methods have gained increasing attention in the reliability literature. The focus of most of the earlier Bayesian work in reliability involved statistical inference and thus the main emphasis was on modeling and analysis. Advances in Bayesian computing after the 90’s have significantly contributed not only to the use of Bayesian inference and prediction but also to the implementation of Bayesian decision-theoretic approaches in reliability problems. In this review we present an overview of Bayesian methods to solve decision problems in reliability some of which involve two or more decision makers with conflicting objectives. We consider problems in areas such as design, life testing, preventive maintenance, reliability certification, or warranty policies. In doing so, we present key aspects of the decision problems, give a brief review of earlier methods and finally discuss recent advances in Bayesian approaches to solve them.