A Multi-Process Production Quality Decision Optimization Model Based on Sampling Estimation and Exhaustive Search

Abstract

This paper proposes a decision-making model that integrates sampling estimation and combinatorial optimization to address quality control and cost optimization in multi-process production systems. First, a sampling estimation method is developed based on hypothesis testing to perform statistical inference on component defect rates, thereby reliably obtaining quality parameters. Building on this foundation, a multi-stage production decision-making model is established, which unifies the inspection and disassembly decisions for components, semi-finished products, and finished goods into discrete variables, and is formulated with the objective of minimizing total cost. For the solution, an exhaustive search algorithm is employed to traverse all decision combinations and obtain the global optimal solution. Additionally, by expanding the defect rate from a deterministic value to a sample estimate, uncertainty is introduced, making the model more closely aligned with real-world production environments. The results indicate that this method can achieve an effective balance among inspection costs, defect handling, and resource recovery, demonstrating good generality and practical value. By integrating statistical inference with discrete optimization methods, this study provides an efficient and feasible modeling and solution approach for quality decision-making in multi-stage production systems.