A multi-state network to evaluate network reliability with maximal and minimal capacity vectors by using recursive sum of disjoint products

This paper applies a multi-state network (MSN) model with multi-state capacity to evaluate network reliability with both maximal and minimal capacity vectors for real-life applications. To be specific, the proposed MSN model can be embedded in the practically related expert systems, especially in project networks, manufacturing, and supply chain. In the early works, the estimated network reliability with maximal and minimal capacity vectors and the exact value for the MSNs were measured based on an interval approach and inclusion and exclusion (IE) principle, respectively. Owing to the computational inefficiency, the early works are inappropriate to be integrated into practical expert systems. In this paper, a more efficient procedure based on the sum of disjoint products (SDP) principle calculates the exact network reliability. Additionally, a recursive function with simplified processes is developed to achieve the efficiency of reliability evaluation. By using a practical project network case with several numerical experiments, efficiency investigation reveals that the SDP-based procedure outperforms the IE-based approach in terms of efficiency under all the experiments. The proposed SDP-based procedure can achieve over 30 times (and reach up to 5,000 times) faster than the IE-based approach. That is, based on the proposed procedure, the reliability evaluation of practical applications such as project management can be implemented.