提出一种无需分布假设的自适应控制图，可早期精准检测多流二元数据异常。
A Nonparametric Adaptive EWMA Control Chart for Binary Monitoring of Multiple Stream Processes
- 基于精确方差推导自适应控制限，避免传统方法对渐近估计的依赖。
- 在目标ARL0为370和500时，中等偏移（δ=0.2）下平均检出时间仅需3-7样本。
- 对不同分布均表现稳健，小偏移下运行长度变异系数低于0.10，适合工业与安全场景。
在统计过程控制中，监控多个独立流的二项比例是一项关键挑战，应用场景涵盖制造到网络安全。虽然EWMA控制图对微小偏移敏感，但现有方法依赖渐近方差近似，导致早期阶段失效。本文提出累积标准化二项式EWMA（CSB-EWMA）控制图，通过推导二元多流数据中EWMA统计量的精确时变方差，实现从首样本起即具统计严谨性的自适应控制限。大量模拟表明，在目标为ARL0=370和500时，最优平滑参数λ与控制限L可实现预期性能。该方法在两种目标下均能快速检测偏移，中等偏移（δ=0.2）时出控平均运行长度（ARL1）降至3-7样本；且在不同数据分布下表现出优异鲁棒性，小偏移时ARL1系数变异（CV）低于0.10，适用于实际工程中的早期异常发现。
原文摘要 · Abstract (English)
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 (λ) 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 (δ=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.
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