Research on Production Decision Optimization Based on Sampling Inspection and Cost Analysis

With the increasing competition in the manufacturing industry, how to optimize the production process to reduce production costs has become a key issue for enterprises. This paper addresses the optimization of production processes in the manufacturing industry, focusing on sampling inspection schemes and production decision-making models. Based on binomial distribution hypothesis testing with unknown incoming defective rates, this paper develops an optimal sampling program by controlling confidence conditions and simulating rejection domains. This approach minimizes detection frequency while maintaining effective quality control. Furthermore, this paper proposes a comprehensive decision equation model that considers various cost factors including parts procurement, assembly, inspection, dismantling, exchange losses, and market sales of finished products. The model dynamically adjusts the inspection proportions of spare parts and finished products, the dismantling ratio of substandard products, and the procurement ratio of two types of spare parts. Through optimization within specified constraints, the model achieves optimal resource allocation. Analysis of empirical data reveals optimal sampling inspection ratios of 0.0797, 0.0438, and 0.0201 for spare parts 1, spare parts 2, and finished products respectively. Additionally, the model yields an optimal dismantling ratio of 0.9511 for defective products, an optimal proportion of 0.5009 for spare parts 1, and a normalized expected profit value of 11.5548.