π€ AI Summary
This study addresses the limitations of existing control charts for early monitoring of multi-stream binary processes, which suffer from inaccuracy due to reliance on asymptotic variance approximations and poor sensitivity to small shifts. To overcome these issues, the authors propose a Cumulative Standardized Binomial EWMA (CSB-EWMA) control chart that derives the exact time-varying variance of the EWMA statistic, enabling adaptive control limits without asymptotic assumptions and ensuring statistical rigor from the very first observation. As the first nonparametric, adaptive, and theoretically rigorous EWMA scheme tailored for multi-stream binary data, the CSB-EWMA achieves substantially improved early detection performance: under in-control average run lengths (ARLβ) of 370 or 500, it reduces the out-of-control ARLβ to 3β7 for moderate shifts (Ξ΄ = 0.2) while maintaining high stability for small shifts (coefficient of variation < 0.10).
π Abstract
Monitoring binomial proportions across multiple independent streams is a critical challenge in Statistical Process Control (SPC), with applications from manufacturing to cybersecurity. While EWMA charts offer sensitivity to small shifts, existing implementations rely on asymptotic variance approximations that fail during early-phase monitoring. We introduce a Cumulative Standardized Binomial EWMA (CSB-EWMA) chart that overcomes this limitation by deriving the exact time-varying variance of the EWMA statistic for binary multiple-stream data, enabling adaptive control limits that ensure statistical rigor from the first sample. Through extensive simulations, we identify optimal smoothing (Ξ») and limit (L) parameters to achieve target in-control average run length (ARL0) of 370 and 500. The CSB-EWMA chart demonstrates rapid shift detection across both ARL0 targets, with out-of-control average run length (ARL1) dropping to 3-7 samples for moderate shifts (Ξ΄=0.2), and exhibits exceptional robustness across different data distributions, with low ARL1 Coefficients of Variation (CV < 0.10 for small shifts) for both ARL0 = 370 and 500. This work provides practitioners with a distribution-free, sensitive, and theoretically sound tool for early change detection in binomial multiple-stream processes.