Belief Universal Generating Function Analysis of Multi-State Systems Under Epistemic Uncertainty and Common Cause Failures

Because of the complexity of engineering systems, and the fact that insufficient data are only available to obtain the precise state probability of components, an extended universal generating function (UGF) based on belief function theory is introduced in this paper to conduct the reliability analysis of multi-state systems (MSSs) with epistemic uncertainty. The behavior of common cause failures (CCFs) is further incorporated, and the occurrence probability of CCFs is evaluated using a weighted impact vector method. A numerical example is used to illustrate how the proposed method works. In addition, a global optimization method is used to obtain the truth interval of the system reliability, and the results are compared with those obtained by using some existing methods. The case study shows that the belief UGF method can effectively avoid the interval expansion problem and the overestimation problem involved in the interval UGF method, and the proposed method can be used to provide a reliable way to evaluate the reliability of MSSs with interval data and CCFs.