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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.<\/jats:p>","DOI":"10.1007\/s00291-025-00831-0","type":"journal-article","created":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T08:22:49Z","timestamp":1755937369000},"page":"355-384","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Overcoming the curse of dimension of the optimal group maintenance policy of a heterogeneous multi-component series system"],"prefix":"10.1007","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5723-9037","authenticated-orcid":false,"given":"Stephane","family":"Barde","sequence":"first","affiliation":[]},{"given":"Young Myoung","family":"Ko","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5161-661X","authenticated-orcid":false,"given":"Hayong","family":"Shin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,23]]},"reference":[{"issue":"4","key":"831_CR1","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1287\/ijoc.2018.0863","volume":"31","author":"A Abbou","year":"2019","unstructured":"Abbou A, Makis V (2019) Group maintenance: a restless bandits approach. 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