Author(s)

Zi’an Lin

Corresponding Author

Zi’an Lin

Abstract

This paper constructs a mathematical model to optimize the production process of enterprises and reduce production costs, and systematically analyzes the relationship between sampling inspection schemes and production decisions. First, a sampling inspection scheme that minimizes the number of inspections is designed to determine whether to accept spare parts with a claimed defective rate of no more than 10%. At the confidence level of 95% and 90%, the central limit theorem is used to approximate the sample proportion distribution, and the minimum sample size is calculated to be 97 and 68 respectively, and the standard z test is used to define the rejection region. Then, the expected cost and expected profit are analyzed, the optimization objective function is constructed, and the simulated annealing algorithm is used to evaluate the unit expected profit under different scenarios. At the same time, the extended model incorporates the defective rate, cost and selling price data of multiple processes and multiple spare parts, so that the unit expected profit reaches 85.653 yuan. In addition, when the defective rate is the sampling inspection result, the decision reanalysis is performed based on the normal distribution random simulation, which verifies the robustness and prediction accuracy of the model. Finally, an optimization scheme based on Bayesian theorem for product impairment estimation and multivariate normal description of defective rate is proposed to improve the competitiveness and decision-making efficiency of enterprises.

Keywords

Z-Test, Simulated Annealing Algorithm, Random Simulation, Geometric Distribution