A Cost Efficient Algorithm for System Reliability Calculation with Aleatory and Epistemic Uncertainties Using Evidence Theory

In reliability calculation of complex system, it is always in the situation that experimental data is inadequate, or information is not complete, which makes the system not only involving aleotory uncertainty, but also epistemic uncertainty. To reduce the cost of reliability calculation, an effective approach with evidence theory is developed. In this approach, the mean of belief and plausibility function is taken as the approximation of system reliability. The discretization methods for uncertain parameters are discussed when system involves only aleatory uncertainty, and involves aleatory and epistemic uncertainties simultaneously, respectively. Algorithms for belief and plausibility function evaluation are proposed for monotonic and non-monotonic system. Four numerical examples with different conditions are studied. Simulation results show that, the proposed method is much more effective than Monte Carlo method without sacrificing the accuracy of resulting reliability, and is a general method which is applicable for various systems with different types of information