Exploring the Puzzles in Comparing Reliability Surrogate Measures for Water Distribution System Design: From the Dual Perspectives of Equal-Cost and Consistency

Various reliability surrogate measures (RSMs) have emerged over last three decades to design water distribution systems (WDSs). However, there has yet to be a consensus on their rationalities. In this work, we proposed a novel dual-perspective framework to examine RSMs’ rationalities, including the equal-cost perspective (ECP) by comparing RSMs’ performance at three comparable equal-cost levels and the traditional consistency perspective (TCP) widely used in other comparative studies. RSMs’ performance was evaluated by the mechanical reliability score (MRS) and the normalized resilience score (NRS). The former compared fewer pipe failures under a snapshot scenario, while the latter considered more comprehensive pipe failures using global resilience analysis. We compared five well-known RSMs from the literature, i.e., Network Resilience Index (NRI), Diameter-Sensitive Flow Entropy (DSFE), Redundancy (REDU), Pipe Hydraulic Resilience Index (PHRI) and Combined Entropy-Resilience Index (CERI). We verified their performance for the multi-objective design of two medium-scale, single-source WDSs, i.e., Hanoi and Fossolo. Results reveal that NRI is the most rational measure. The rankings from NRS are similar to those from MRS under the ECP; however, the two rankings vary significantly under the TCP. The ECP is more reasonable than the TCP because it measures network resilience and reliability from practical performance. We recommend using the MRS+ECP framework to compare RSMs since it reflects the critical aspect of global resilience with lower computational overhead. Furthermore, some meta information, e.g., nodal pressure head and demand, has the most significant impact on the rankings of RSMs, inspiring the development of new and better RSMs.