The research focuses on the reliability analysis of a complex system comprising two inter-connected subsystems. Each subsystem consists of three identical units arranged in parallel. The operational policy employed is the 1-out-of-3: G policy, which means that as long as at least one unit is operational in each subsystem, the system as a whole remains functional. The failure rates of the units within the subsystems are consistent and follow an exponential distribution. To address unit failures and repair them, the Gumbel-Hougaard copula repair method is employed. The research investigates various reliability metrics, including system availability, system reliability, mean time to failure (MTTF), and sensitivity analysis. The researchers employ stochastic theory, differential equations, and supplementary variables to model and analyze the reliability behavior of the system. Moreover, the model’s findings can guide decision-making processes related to system design, component selection, and maintenance strategies. System engineers and managers can utilize the insights gained from the reliability analysis to optimize the system’s performance, enhance its reliability, and reduce costs associated with maintenance and repair.