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.

Currently, supply chain networks can span the whole world, and any disruption of these networks may cause economic losses, decreases in sales and unsustainable supplies. Resilience, the ability of the system to withstand disruption and return to a normal state quickly, has become a new challenge during the supply chain network design. This paper defines a new resilience measure as the ratio of the integral of the normalized system performance within its maximum allowable recovery time after the disruption to the integral of the performance in the normal state. Using the maximum allowable recovery time of the system as the time interval under consideration, this measure allows the resilience of different systems to be compared on the same relative scale, and be used under both scenarios that the system can or cannot restore in the given time. Two specific resilience measures, the resilience based on the amount of product delivered and the resilience based on the average delivery distance, are provided for supply chain networks. To estimate the resilience of a given supply chain network, a resilience simulation method is proposed based on the Monte Carlo method. A four-layered hierarchial mobile phone supply chain network is used to illustrate the resilience quantification process and show how network structure affects the resilience of supply chain networks.

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.