Reliability analysis of systems using belief functions theory to represent epistemic uncertainty.

Summary There are different ways to classify uncertainty or its sources. The most common distinction is to divide uncertainty into two types: random uncertainty and epistemic uncertainty. The first type is irreducible and due to the natural variability of random phenomena. The second type is reducible and due to a lack of knowledge that can be reduced by making more efforts (collecting more data, consulting experts, accelerated testing. . . ). Recently, several authors have begun to challenge the use of classical probabilities to deal with these two types of uncertainties. New theories that deal with the different types of uncertainties have appeared. These theories are able to represent and propagate both random and epistemic uncertainty. Among these theories, the theory of belief functions is exploited in this manuscript to handle uncertainties in system reliability studies. Various issues related to reliability studies in the presence of epistemic uncertainties, as well as reasons why probability theory should not be used in this case, are discussed. The manuscript introduces methods for representing reliability data and combining expert opinions. Then, it presents several methods for propagating uncertainty about the reliability of components at the system level. An important result of these methods is that the lower (upper) bound on system reliability depends only on the lower (upper) bounds on component reliability, and that the belief and plausibility functions are additive for the collection of minimal paths and minimal cuts.