Research on Multi-Stage Production Quality Optimization Based on Dynamic Programming and Integer Programming

In modern manufacturing processes, the complexity of multi-stage and multi-process quality management necessitates the optimization of quality control strategies at each production stage to meet stringent quality requirements while enhancing operational efficiency. This study focuses on key indicators such as the substandard rate of defective components and detection efficiency, providing methods to determine the optimal production stage. Initially, addressing the sampling inspection issue, this study determines the optimal sample size and designs a sampling inspection plan by constructing statistics and the power function. If the goal is to assert with 95% confidence that the defect rate of components exceeds the nominal value, this method yields a preferable sample size range of 98 to 435. Subsequently, this study focused on the direction of integer programming in the field of multi-stage decision-making and formulated a practical and feasible implementation plan through specific examples. During the research process, it deeply analyzed the application of dynamic programming in multi-stage production decision-making scenarios. In response to the complex and changeable factors in the actual manufacturing production situation, it further optimized and improved the relevant methods to enable them to serve the manufacturing production process more accurately and effectively. Through this work, the paper offers a reference methodology for achieving effective product quality control in manufacturing settings.