Optimal Sampling and Decision-Making Strategies in Multi-Stage Manufacturing Processes

In the process of product manufacturing, the scientific and rational design of sampling inspection and production decision-making strategies is of significant practical importance for enhancing corporate profits. This paper constructs a sampling inspection model based on statistical sampling and hypothesis testing theories. It employs sequential interval estimation to determine the minimum sample size that meets reliability requirements, thus providing an optimal sampling inspection plan. Furthermore, decision trees and 0-1 integer programming are used to develop cost models and profit optimization models for each stage of production, culminating in the design of an optimal decision-making strategy through the state transition equations of dynamic programming.