Currently, the use of industrial seawater reverse osmosis desalination (ISROD) plants has increased in popularity in light of the growing global demand for freshwater. In ISROD plants, any fault in the components of their control systems can lead to a plant malfunction, and this condition can originate safety risks, energy waste, as well as affect the quality of freshwater. This paper addresses the design of a fault detection and isolation (FDI) system based on a structural analysis approach for an ISROD plant located in Lima (Peru). Structural analysis allows obtaining a plant model, which is useful to generate diagnostic tests. Here, diagnostic tests via fault-driven minimal structurally overdetermined (FMSO) sets are computed, and then, binary integer linear programming (BILP) is used to select the FMSO sets that guarantee isolation. Simulations shows that all the faults of interest (sensors and actuators faults) are detected and isolated according to the proposed design.