A Note on Reliability Analysis of Multi-Stage Manufacturing Systems with Controlled Capacity Release

Modern manufacturing systems are becoming increasingly complex as production lines integrate multiple interconnected processes. In multi-process mechanical manufacturing systems, deviations in upstream operations often propagate downstream, resulting in performance degradation and reliability loss in subsequent machines. To mitigate such degradation, this paper introduces the concept of release-controlled capacity, where each machine’s operational capacity can be dynamically adjusted or released in response to system conditions. Continuous-time Markov chains (CTMCs) capture the stochastic degradation of machines by modeling transitions through discrete performance states, where systems can only move from higher to lower capacity due to wear or failure. Quality–Reliability (Q-R) dependency quantifies how upstream product quality deviations accelerate downstream machine degradation rates, linking product quality to system reliability. These two concepts provide the theoretical foundation for the proposed quality state-space model. A Controlled Capacity Release (CCR) mechanism allows for the dynamic activation of reserved resources to compensate for performance loss. It is driven by a combination of hardware resources and a control system. Unlike traditional "pure-death" models that only account for monotonic degradation, the proposed model incorporates CCR as probabilistic recovery transitions to higher-capacity states, effectively capturing the system's ability to restore performance through automated control or buffer utilization.

The proposed approach is validated through numerical experiments in a multi-stage manufacturing system case study. Results demonstrated that the CCR mechanism significantly slows down the rate of reliability degradation compared to traditional models. Furthermore, experimental results revealed that while higher recovery rates improve system stability, the benefits exhibit a diminishing-return effect due to system coupling and Q-R dependency.