## 5 Discussion and Conclusions  
To identify and prioritize the critical pipes in a WDN, an element-based simulation approach is proposed. The element-based criticality is measured using four criticality indexes, including supply shortage (\(SS\)), economic value loss (\(EVL\)), pressure decline (\(PD\)), and water age degradation (\(WAD\)). These indexes measure different aspects of performance degradation, specifically social, economic,  
Figure 11: Comparison of the four criticality indexes with Resilience Index (RI) for Network 1.  
Figure 12: Comparison of the four criticality indexes with Resilience Index (RI) for Network 2.  
hydraulic, and water quality, respectively. Evenly weighting the four indexes, the OVERALL criticality is calculated to identify and prioritize the critical pipes.  
For demonstration, the proposed indexes are applied to four networks that have different characteristics. The results show that each index representing different aspects yields variable criticality ranks per pipes. The individual results are then combined into a single criticality value to provide the overall assessment of criticality of individual pipes. The network type also affects the criticality results; here, we have compared four different networks from the densely loop to the branch-loop hybrid type. Generally, it was found that the pipes with large sizes and serving high-demand nodes tend to show greater criticality. However, the topological parameter (DoN) shows a certain relation with the pipe criticality depending on the network type. For verification of the proposed indexes, a comparison test with the well-known RI was conducted. Both results indicate similar patterns and commonly identify the critical pipes. It is noteworthy that the proposed indexes quantify four distinct aspects of WDNs service, while the RI only deals with the hydraulic performance. Thus, the proposed indexes are likely to improve the criticality assessment of a pipe network.  
The proposed element-based simulation approach can be used to identify the critical pipes in a network, and using this information, the area with a high maintenance priority can be determined to maintain network function. Overall, the proposed element-based index can be utilized to setup maintenance scheduling for preparedness of potential failure events. The proposed approach can be further improved for assessment of other components in WDNs, and various operation aspects can also be added in future development.  
Conceptualization, M.S.M. and D.K.; methodology, M.S.M.; software, M.S.M. and G.J.; investigation and data analysis, M.S.M., G.J., and D.K.; writing--original draft, M.S.M. and G.J.; writing--review and editing, M.S.M., G.J., and D.K.  
This work was supported by (1) the Korea Environment Industry & Technology Institute (KEITI) through the Advanced Water Management Research Program, funded by the Korea Ministry of Environment (Grant 83079) and (2) the EDISON\" Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2017M3C 1A6075016). *Education-research Integration through Simulation On the Net.  
The authors declare no conflict of interest.