Advanced Stochastic Modeling for Series Production Processes: A Markov Chains and Queuing Theory Approach to Optimizing Manufacturing Efficiency

The study presents an integrated stochastic modeling framework that combines Markov chains and queuing theory to optimize production efficiency in a metallurgical machining process. The model captures the dynamic behavior of key manufacturing stages, milling, drilling, reaming, and packing, by representing rework, inspection, and waste as distinct probabilistic states. Effective arrival rates and service rates are computed to evaluate machine utilization, total processing time, and throughput. The proposed approach was applied to an industrial case study, where the results showed that reprocessing activities increased the total cost per conforming unit by approximately 0.3% and affected overall system performance. By adjusting machine allocation and minimizing rework probabilities, the model demonstrated measurable improvements in cycle time and cost efficiency. This integrated methodology provides a practical decision-support tool for optimizing production flow, balancing resource utilization, and reducing the financial impact of nonconformity in continuous manufacturing environments.