Owing to the impressive development in the electricity distribution network, the managers of the system should be able to handle the costs of the network effectively. The practical implementation of the reliability-centered maintenance is one of the ways to address this concern. In this paper, we initially use the multi-criteria decision-making method of gray relative analysis to prioritize failure modes and obtain their risk factor in the network. Various failure modes in network equipment such as insulators, jumpers, cutout fuses, switches, transformers, and the cables are considered. Then, to select optimal strategies for each failure mode, we present an optimization based on the energy not supplied of electrical distribution feeder, the maintenance cost, the outage cost, the safety cost and the risk factor of failure modes. Hotline, coldline, and neutral are among the strategies to be implemented in the current research. To show the effectiveness of the proposed method, we utilize various scenarios to investigate the impacts of maintenance duration, hotline safety costs and practical restrictions on the results. Findings indicate that total maintenance costs, compared to those of the business as the usual strategy, can be reduced by at least 7% when the propose method is applied.