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In water distribution networks (WDN) equipped with pump as turbines (PATs), in addition to water pressure problems, energy production by PATs is also necessary in abnormal conditions. Reliability indices are the most important parameters in determining the efficiency of systems when components fail. In this research, while proving the correlation weakness of a number of previous indices with the energy, a new energy reliability index is introduced, and it’s integrated with previous reliability indices. Since checking the performance of networks from different aspects leads to increasing accuracy and reducing design and operation costs, in the following, the correlation of each of the integrated indices with the performance indices (PI) of adequacy, equity, energy, adequacy- equity, adequacy-energy, equity-energy, and total are calculated for two WDNs. Finally, the most critical network pipes for repair and …