Nonparametric Adaptive Charting Schemes for Monitoring Variability of Count Data Based on a New Categorization Algorithm

Monitoring count data is critical across many application domains. Most existing control charts for such data rely heavily on parametric models, particularly the Poisson distribution. However, these models often perform poorly in practice due to the presence of confounding factors, leading to unreliable monitoring outcomes. Moreover, while some nonparametric control charts have been proposed in the literature, they primarily focus on detecting shifts in the mean. Monitoring variability in count data, however, is equally important and has received comparatively less attention. In this article, we enhance Li's nonparametric control chart to improve its effectiveness in monitoring count data. The proposed adaptive control chart employs a central‐outward categorization strategy that preserves the rank information of the original data. To further improve classification accuracy, we introduce a novel interval segmentation algorithm. In addition, we develop a self‐starting version of the adaptive chart, eliminating the need for historical reference data. Our control charts address key limitations in existing variance monitoring methods for count data. Numerical studies and real‐world case analyzes demonstrate that the proposed approach offers greater efficiency and stability compared to several established techniques.