A Sampling Method of Sequential Tests with Sample Size Limit Under Poisson Distribution

Sequential inspection is a technique employed to monitor product quality during the production process. For smaller batch sizes, the Acceptable Quality Limit (AQL) inspection theory is typically applied, whereas for larger batch sizes, the Poisson distribution is commonly utilized to determine the sample size and rejection thresholds. However, due to the fact that the rate of defective products is usually low in actual production, using these methods often requires more samples to draw conclusions, resulting in higher inspection time. Based on this, this paper proposes a sequential inspection method with a fixed upper limit of sample size. This approach not only incorporates the Poisson distribution algorithm, allowing for rapid calculation of sample size and rejection thresholds to facilitate planning, but also adapts the concept of sequential inspection to dynamically modify the sampling plan and decision-making process. This method aims to decrease the number of samples required while preserving the inspection's efficacy. Finally, this paper shows through Monte Carlo simulation that compared with the traditional Poisson distribution algorithm, the sequential test method with a fixed sample size upper limit significantly reduces the number of samples compared to the traditional Poisson distribution algorithm, while maintaining effective inspection outcomes.