A Reliability Evaluation Framework for Stochastic-Flow Hybrid Production Network with Automatic and Manual Production Lines

Previous studies on stochastic-flow production networks have typically assumed either fully automatic or fully manual workstations. However, real-world production systems often integrate both machines and human workers. Additionally, rework operations are also common; in certain sectors, such as surface mount technology (SMT), these tasks remain manual due to the complexity and flexibility required for small-batch production in small and medium-sized enterprises. This study focuses on a stochastic-flow hybrid production network (SFHPN) consisting of two production lines--one automatic and one manual, where all rework operations are handled by the manual line. A reliability evaluation framework is proposed, incorporating an algorithm designed to determine the minimal capacity of each workstation and to evaluate the satisfaction probability representing the system’s reliability. The proposed model captures a fundamental yet practical hybrid production structure that reflects the cooperative interaction between automation and manual operations. This framework enables production managers to enhance decision-making, operational efficiency, and overall system stability.