An Improved Sum-of-Disjoint-Products Technique for Symbolic Multi-State Flow Network Reliability

Many real-world systems, such as electric power and transportation, satisfy the flow conservation law, and can be considered to be multistate flow networks (MFN). Reliability is a popular index for evaluating MFN performance, and the sum-of-disjoint products (SDP) technique is a popular tool for evaluating MFN reliability. An improved SDP (iSDP) is proposed in this study by adding simplification procedures to reduce the number of multiplications and summations to increase the efficiency of the SDP; the validity and effectiveness of the iSDP is also demonstrated in this study. The iSDP´s computational complexity is also analyzed, and one benchmark example is given to illustrate how MFN reliability is determined using the proposed iSDP method. In addition, computational experiments with two MFN are conducted to test the performance of the iSDP method, along with comparisons to the existing best-known SDP method.