Abstract: This paper considers a multi-state complex repairable system with priority repair discipline, which includes two classes of components, denoted by L₁ and L₂. L₁ consists of n different types of components in series, whereas L₂ contains only one component. The system fails if any component in L₁ fails. If the component in L₂ fails, it does not lead to a complete failure, but reduces the effciency of the system. It is assumed that the working time to the two types of components follows different exponential distributions, while the repair time of the repairman follows a general distribution. We derive the system's main steady-state reliability indices using probability analysis, the Laplace transform method, and Tauber's theorem. The instantaneous reliability indices of the system are then estimated by applying Monte Carlo simulation, and the numerical results of special cases verify the correctness of the conclusion. On this basis, this paper also investigates the influence of system parameters on system reliability measures. Furthermore, we analyze the sensitivity of the instantaneous reliability and MTTFF with respect to each parameter, and we derive the expected profit rate, thereby providing theoretical guidance for reliability engineers and decision-makers.