An Evidence Theory-based Algorithm for System Reliability Evaluation under Mixed Aleatory and Epistemic Uncertainties

For the reliability evaluation of a complex system, the aleatory uncertainty and epistemic uncertainty always exist at the same time because of the inadequate experimental data and the incomplete information. To reduce the computational cost of the reliability evaluation, an effective method based on evidence theory was developed. In this method, the mean of the belief measure and the plausibility measure was taken as the approximation of the system reliability. The discretization methods for uncertain parameters were discussed in the cases of only aleatory uncertainty was involved in the system, and mixed aleatory and epistemic uncertainties were involved, respectively. Algorithms of the evaluations of belief and plausibility functions were proposed for monotonic and non-monotonic systems. Four numerical examples under different conditions were studied. Simulation results showed that, the proposed method was much more effective than Monte Carlo method without sacrificing the accuracy of the resulting reliability. It was a general method suitable for various systems with different types of information.