Determining the Optimal Parameters for Acceptance Sampling in Quality Control

The paper addresses the problem of determining optimal values for acceptance sampling parameters, which are crucial for product quality control. Single-stage sampling for inspection by attributes is considered. The purpose of acceptance sampling is to determine the extent to which the quality of a lot provided by the supplier conforms to the quality level agreed upon with the consumer. In accordance with government standards, a sampling plan is developed to ensure satisfactory levels of risk for both the supplier and the consumer. This is achieved by determining the optimal sample size and acceptable number of defects (acceptance number). Solving this problem leads to a system of inequalities. The challenge is that the resulting system is non-linear and cannot be solved using standard numerical methods. Therefore, this work proposes a combinatorial search algorithm based on exploring different sample sizes and evaluating the range of values for the acceptance number using probability theory. The efficiency of the obtained algorithm under different parameters of the task has been investigated experimentally. The work also provides an approbation of the proposed algorithm using the example of acceptance sampling of genetic material of spruce seeds based on cytogenetic indicators for the selection of mother plants that produce fast-growing offspring. This is important in carrying out greening activities for the selection of coniferous plants that are drought-resistant and winter-hardy.