**5. Conclusions**

In this study, correlations between hydraulic measures and reliability indices were analyzed to evaluate the ability of reliability indices to reflect system performance. To that purpose, six (hydraulic) measures of redundancy, robustness, and serviceability and nine reliability indices based on hydraulic, topological, entropic, and mixed approaches were selected. Correlation analyses were performed using the 17 optimally designed hypothetic WDNs under three abnormal operation scenarios. To obtain a comprehensive evaluation of individual indices, an MCDA based on WSM was performed as a post-analysis. Based on the results obtained in the study, the following conclusions can be drawn:


Prior to using any reliability index for the design and operation of a WDN, it is essential to select an adequate reliability index suitable for the goals of the designer/operator, and the results of this study can contribute to that purpose. In addition, the proposed comparative analyses are expected to be useful in research on index development that can better reflect various network performances. Future study should consider the needs of water managers for scenario development reflecting real operational conditions and the selection of reliability indices and hydraulic measures. Further comparative analyses, including various reliability indices and hydraulic measures for a number of WDNs with diverse sizes and layouts, are a fruitful area to pursue as a future study. Through the proposed comparative analysis, it is anticipated that the best fit reliability indices can be suggested and developed for quantification of WDN performance.

**Author Contributions:** Conceptualization, G.J. and D.K.; methodology, G.J. and D.K.; software, G.J.; validation, D.K.; formal analysis, G.J. and D.K.; writing—original draft preparation, G.J.; writing—review and editing, D.K.; supervision, D.K.; funding acquisition, D.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT—Ministry of Science and ICT) (No. NRF-2020R1A2C2009517).

**Conflicts of Interest:** The authors declare no conflict of interest.
