Abstract Indirect approaches based on minimal path vectors (d-MPs) and/or minimal cut vectors (d-MCs) are reported to be efficient for the reliability evaluation of multistate networks. Given the need to find more efficient evaluation methods for exact reliability, such techniques may still be cumbersome when the size of the network and the states of component are relatively large. Alternatively, computing reliability bounds can provide approximated reliability with less computational effort. Based on Bai’s exact and indirect reliability evaluation algorithm, an improved algorithm is proposed in this study, which provides sequences of upper and lower reliability bounds of multistate networks. Novel heuristic rules with a pre-specified value to filter less important sets of unspecified states are then developed and incorporated into the algorithm. Computational experiments comparing the proposed methods with an existing direct bounding algorithm show that the new algorithms can provide tight reliability bounds with less computational effort, especially for the proposed algorithm with heuristic L1.

中文翻译：

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一种改进的多状态网络可靠性边界算法

摘要 据报道，基于最小路径向量 (d-MP) 和/或最小切割向量 (d-MC) 的间接方法对于多状态网络的可靠性评估是有效的。鉴于需要找到更有效的精确可靠性评估方法，当网络规模和组件状态相对较大时，此类技术可能仍然很麻烦。或者，计算可靠性界限可以以较少的计算工作量提供近似的可靠性。本研究在白氏精确和间接可靠性评估算法的基础上，提出了一种改进算法，该算法提供了多状态网络的可靠性上下界序列。然后开发具有预先指定值的新颖启发式规则以过滤不那么重要的未指定状态集并将其合并到算法中。