Maintenance optimization of multistage manufacturing systems with reliability and quality interaction

We study the optimal maintenance policy for multi-station manufacturing processes (MMPs) under the joint consideration of system reliability and product quality. These two factors interact through the Quality-Reliability Chain (QR-Chain) effect, where poor incoming product quality accelerates downstream tool wear, while station degradation can impair the quality of outgoing products. To the best of our knowledge, this is the first study to derive an optimal maintenance strategy for MMPs while explicitly considering QR-Chain effects. We formulate our problem based on a Partially Observable Markov Decision Process (POMDP). Unlike conventional POMDPs, our model has the property of interdependence between latent and observable state dynamics, where the latent quality states affect the transition of observable degradation states, and observed degradation states inform the belief updates of latent quality. We establish structural results on the optimal policy and make new theoretical contributions that extend the frontier of standard POMDP applications in maintenance optimization. Numerical experiments demonstrate the effectiveness of our model and validate operational insights in real-world production systems.