Production, maintenance, and quality represent the three primary tasks in manufacturing systems. Previous studies have predominantly focused on optimizing these tasks separately or jointly optimizing two of them. However, it is worth noting that these tasks exhibit mutual interaction, and models failing to consider them simultaneously cannot achieve global optimality. Therefore, this paper aims to develop a quality-centered production and maintenance scheduling methodology (QPMSM) for multi-machine and multi-product manufacturing systems. Specifically, a delivery time-based production scheduling strategy is introduced to emphasize the impact of maintenance activities. A quality loss model is developed to characterize the mapping relationship between quality deterioration and component degradation. Furthermore, a well-designed maintenance strategy determines the optimal timing and frequency of maintenance activities to improve system performance and reduce quality deterioration. Building upon this foundation, an integrated model is proposed to concurrently optimize production scheduling, maintenance planning, and quality control tasks to minimize the overall system cost. The effectiveness of the proposed QPMSM in terms of cost-savings has been verified using a designed hybrid meta-heuristic algorithm, providing a viable approach for simultaneous optimization.