<p>This study addresses the challenge of optimizing maintenance strategies for multi-component series systems with economic interdependencies. We propose a new model that incorporates each component failure rates into an average cost Markov Decision Process (MDP) framework. To manage the inherent complexity of non-Markovian failure rates often encountered in reliability, we utilize phase-type approximation techniques. These approximations enable accurate estimation of transition probabilities within the MDP framework, allowing for a more effective analysis of optimal maintenance policies. To counteract the computational challenges posed by the high dimensionality of both the state and action spaces, we conduct a comprehensive structural analysis of the optimal group maintenance policy. This analysis significantly reduces the combinatorial action space to a manageable linear form while preserving the optimality of the solution for multi-component series systems. In addition, a control-limit policy is proposed based on the in-depth structural analysis. Finally, the optimal group maintenance policy and the introduced sub-optimal control-limit policies are analyzed through extensive Monte Carlo simulations.</p>