The Bayes predictive approach in reliability theory

Abstract

A strong motivation for reliability analyses is to support decision-making relative to the construction and operation of systems involving an economic/environmental risk. The Bayes approach to making decisions in face of uncertainty about mission survival is presented step by step. The authors show how the decision maker defines his own predictive probability distribution on the system time to failure and ranks the couples (decision taken, observed value of system failure time) by means of a loss function. They also introduce the minimum-expected-loss principle as a leading criterion for decision making. Finally, they address the more general case in which the final decision can be delayed in favor of collecting more information and derive the optimal termination procedure for life testing. For selecting the best course of action in a Bayes reliability frame there is neither need nor room for estimation of probability distribution parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>