4.2.2. Performance-Based MCDA

Table 8 shows the MCDA results of nine indices according to the system performance. For system redundancy quantification, the hydraulic indices (RI, MRI, and API) and two mixed indices (RRI, and NRI) showed great performance in all scenarios. Regarding the robustness context, the overall correlation coefficients are relatively low, which indicates that the applied indices are inadequate to represent the system robustness under the applied scenarios. For measuring system serviceability, the hydraulic indices and PHRI, showed relatively good results.

Finally, the combined MCDA results can be obtained via the averages of Tables 7 and 8 (assuming equal weights for WSM). As seen, among the applied nine indices, the hydraulic indices (RI, MRI, and API) and the hydraulic-based mixed indices (RRI, and NRI) showed high correlation coefficients (i.e., 0.94) and are considered as the optimal indices to quantify the system performance under the applied abnormal scenarios and hydraulic measures.


**Table 8.** Correlation coefficients obtained by performance-based MCDA.

Note: The values highlighted in yellow indicate high correlation coefficient of 0.95 or higher.
