###### Abstract  
The power system and the water system are two important infrastructures of human society that are closely related and interdependent. However, the reliability problems of the power system and water system are becoming more and more prominent. To better reveal the impact of the complex coupling relationship between the power system and the water system on the reliability of the Integrated Electricity-Water System (IEWS), this paper investigates a reliability evaluation method of the IEWS based on multi-state models of equipment in the water system. Firstly, a multi-state reliability model is established based on the failure mechanism of equipment in the water system, such as pipes and Reverse Osmosis (RO) desalination plants. Secondly, combined with the multi-state model of equipment in the water system and the Markov chain Monte Carlo (MCMC) method, the IEWS reliability evaluation method is established. Finally, two IEWSs with different scales are simulated to verify the validity and adaptability of the proposed model. a pacs: 12.38.-b, 12.38.-b, 12.  
with the demand for water, which is used not only for drinking, but also for irrigation and industry, for example, providing cooling water for power plants. Therefore, the failure of equipment in the water system may lead to a significant increase in the overall power consumption of the water system, thereby increasing the operating pressure of the power system, and it may also lead to an insufficient supply of cooling water for thermal power generating units, with component failure spreading to the power system, thereby affecting the reliability of the power system [10]. In this situation, it is imperative to propose a reliability evaluation approach for the IEWS in order to guarantee the safe operation of the system and to give system planning and operation a quantitative foundation for decision making. The failure mechanisms of equipment in the WS are very complex, and there is strong coupling between the power system and water system; therefore, the key challenge to address is how to construct an accurate equipment reliability model for the WS to accurately quantify the reliability of the electricity and water supply. However, research on IEWS reliability evaluation is lacking. The WS involves water production, transmission, and storage, as well as key equipment such as desalination plants, water pipes, pumps, reservoirs, and water valves [11]. Reference [11] investigated the mechanical and hydraulic reliability of the WS by using the minimum cut-set method, which establishes a normal-shutdown model of water supply pipes. However, the water supply capacity of the WS is closely related to the leakage state of water supply pipes [7], and the two-state model obviously cannot accurately portray the actual operating conditions of the system, overestimating WS reliability. References [12; 13] analyzed the optimal scheduling of the IEWS, but the model of RO desalination is simple and did not establish a multi-state reliability model for RO desalination plants, ignoring the impact of component failure in RO desalination on IEWS optimal scheduling. Reference [14] considered the coupling characteristics of the IEWS and analyzed the vulnerability of the power system, but it did not consider the reliability indices of the IEWS, making it difficult to ascertain the level of reliable energy supply of the IEWS. By conducting simulation experiments on a realistic IEWS, the authors of [15] have analyzed the impact of cascading failures of the power system on water supply shortages under different maximum power line capacities and water demand conditions, and they have demonstrated that the urban WS has a strong dependence on the reliability of the power network. However, the article neglected the impact of WS failures on the reliability of the power system. It can be seen that there is a lack of effective IEWS reliability evaluation methods to quantify the level of IEWS electric and water load supply reliability.