Reliability-centered maintenance (RCM) as a subset of the reliability assessment problems, is a powerful tool for enhancing reliability, and subsequently achieving the customers higher satisfaction. However, deterministic RCM models could scarcely guarantee global optimality and feasibility of their solutions with real-world uncertain failure rates. In this paper, a robust model is proposed to consider the impact of failure rate uncertainty in the RCM scheduling problem, followed by a two-stage robust model development. The two-stage robust model is solved using Benders decomposition (BD) and outer approximation (OA) algorithms. The proposed model and solution method are applied to both educational RBTS2 system and real-size Finnish Distribution System, followed by demonstration of a higher financial and reliability performance, compared to that of the deterministic model. Sensitivities of the costs, available budget, uncertainty interval and computational time are analyzed and discussed, to conclude the paper.