Measuring system reliability by a reasonable metric is a basic problem in reliability engineering. Since the real systems are usually uncertain random systems which is affected by both aleatory and epistemic uncertainties, the existed reliability metrics may not work well. This paper aims to develop 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 mainly copes with aleatory uncertainty, or uncertainty theory-based reliability, which mainly 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 some system belief reliability formulas for different systems configurations. To further illustrate the formulas, a simple case study is finally performed in this paper.

Model-based reliability analysis and assessment methods rely on models, which are assumed to be precise, to predict reliability. In practice, however, the precision of the model cannot be guaranteed due to the presence of epistemic uncertainty. In this paper, a new reliability metric, called belief reliability, is defined to explicitly account for epistemic uncertainty in model-based reliability analysis and assessment. A new method is developed to explicitly quantify epistemic uncertainty by measuring the effectiveness of the engineering analysis and assessment activities related to reliability. To evaluate belief reliability, an integrated framework is presented where the contributions of design margin, aleatory uncertainty, and epistemic uncertainty are integrated to yield a comprehensive and systematic description of reliability. The developed methods are demonstrated by two case studies.