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.

Reliability analysis and trade-offs between safety and cost with insufficient data represent an inevitable problem during the early stage of structural design. In this paper, efficient uncertainty theory-based reliability analysis and a design method are proposed under epistemic uncertainty. The factors influencing the structure are regarded as uncertain variables. Based on this, a new metric termed uncertain measure is employed to define an uncertainty reliability indicator (URI) for estimating the reliable degree of structure. Two solving methods, namely, the crisp equivalent analytical method and uncertain simulation (US) method, are introduced to calculate the URI and acquire reliability. Thereafter, a URI-based design optimization (URBDO) model is constructed with target reliability constraints. To solve the URBDO model and obtain optimal solutions, crisp equivalent programming and a genetic-algorithm combined US approach are developed. Four physical examples are solved to verify the adaptability and advantage of the established model and corresponding solving techniques.

Resilience, the ability of a system to withstand disruptions and quickly return to a normal state, is essential for a low-Earth-orbit satellite communication system (LEO-SCS), as its large number of satellites, may encounter various disturbances. As a developing system with asymmetrical and insufficient data, it is with both aleatory and epistemic uncertainties, which renders existing resilience measures inapplicable. This paper utilizes uncertainty theory to define belief instantaneous availability, based on which a new resilience measure for the LEO-SCS is proposed. As the resilience is mainly determined by the dynamic and uncertain characteristics of an LEO-SCS, an uncertain satellite network evolution model is developed to describe its operating patterns, and an evaluation method is proposed to estimate its resilience. To illustrate our proposed uncertain theory-based resilience evaluation method, an LEO-SCS case with 48 satellites is studied, and its resilience values under different backup strategies are compared to assist in system design decisions.