Optimal design of production decisions based on probabilistic and statistical models

Abstract

This paper conducts an in-depth study on a series of decision-making problems faced by a certain enterprise in the production process of electronic products, such as the defective rate, inspection and disassembly. By optimizing the sampling, inspection and disassembly strategies in the production process, the enterprise's profit and production efficiency are maximized. Firstly, a sampling inspection plan is designed. For the two cases of 95% confidence and 90% confidence, a hypothesis testing problem is established. By utilizing the mutually restrictive relationship between inspection cost and hypothesis testing effect, a decision function is established, and the optimal sample size is obtained. Secondly, for four decision-making problems: (1) whether spare parts 1 are inspected; (2) whether spare parts 2 are inspected; (3) whether finished products are inspected; (4) whether unqualified finished products are disassembled, the properties of binomial distribution and geometric distribution are used. Based on parameters such as the defective rate, purchase unit price and inspection cost, a cost-benefit analysis model is established. For six different situations, specific decision-making plans, decision-making basis and corresponding index results are given with the standard of maximizing expected profit. The experimental results show that the method proposed in this paper can provide the enterprise with a set of decision-making plans based on probability and statistical models, helping it to reasonably select sampling, inspection and disassembly strategies when facing different production conditions, and improve resource utilization and economic benefits.