Belief Reliability for Uncertain Random Systems

Measuring system reliability by a reasonable metric is a common problem in reliability engineering. Since real systems are usually uncertain random systems affected by both aleatory and epistemic uncertainties, existing reliability metrics are unreliable. This paper proposes a general reliability metric, called belief reliability metric, to cope with the problem. In this paper, the belief reliability is defined as the chance that a system state is within a feasible domain. Mathematically, the metric can degenerate to either probability theory-based reliability, which copes with aleatory uncertainty, or uncertainty theory-based reliability, which considers the effect of epistemic uncertainty. Based on the proposed metric, some commonly used belief reliability indexes, such as belief reliability distribution, mean time to failure, and belief reliable life, are introduced. We also develop system belief reliability formulas for different systems configurations. To further illustrate the formulas, a real case study is performed.