Belief Reliability Distribution Based on Maximum Entropy Principle

Abstract

Belief reliability is a new reliability metric based on the uncertainty theory, which aims to measure system performance incorporating the influences from design margin, aleatory uncertainty, and epistemic uncertainty. A key point in belief reliability is to determine the belief reliability distribution based on the actual conditions, which, however, could be difficult when available information is limited. This paper proposes an optimal model to determine the belief reliability distribution based on the maximum entropy principle when $k$ th moments of what can be obtained. An estimation method using linear interpolation and a genetic algorithm is subsequently applied to the optimal model. When only the expected value and the variance are available, the optimal results are in accordance with the maximum entropy principle. It could be observed in the sensitivity analysis that the accuracy of the optimal results is a decreasing function of the width of variances and an increasing function of the number of interpolation points. Therefore, researchers could adapt to different widths of variances and requirements of accuracy by adjusting the number of interpolation points. It could be concluded that this new method to acquire belief reliability distribution is important in the application of belief reliability.