Research on Production Quality Control Based on Sampling Inspection Model and Expected Cost Optimization Algorithm

This study explores production quality control based on a sampling inspection model and an expected cost optimization algorithm. First, a sampling inspection model is established, assuming the defect rate follows a binomial distribution. Using z-tests or t-tests, hypotheses are formulated to check whether the defect rate of a batch of parts exceeds the specified threshold. By determining the sample size and conducting power analysis, the model controls Type I errors (rejecting a good batch) and Type II errors (accepting a defective batch), and simulates the sampling process to decide whether to accept a batch. Next, a cost optimization model is proposed to optimize production inspection and handling decisions. Through dynamic programming and expected cost analysis, the impact of different inspection strategies on total production costs and product quality is quantified. The study simulates six different production conditions. Finally, by comparing the total costs and defect rates of 16 different combinations of inspection and disassembly strategies, the optimal strategy is determined. These strategies include whether to inspect part 1, part 2, and the final product, as well as whether to disassemble defective products. This analysis allows for determining the optimal sample size, accurately screening qualified batches, improving inspection efficiency, reducing misjudgments, and lowering inspection costs and time investment.