Haar‐EWMA: A Two‐Channel Control Chart for Robust Mean‐Shift Detection Under Non‐Normality

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ABSTRACT This study proposes Haar‐EWMA, a two‐channel exponentially weighted moving average monitoring framework based on a one‐level sliding Haar pair mapping for robust mean‐shift detection under non‐normal process distributions. For t = 2,…, n, the level channel is defined as ​ and is monitored using limits ​, while the detail channel is defined as ​ and provides auxiliary diagnostic information. To ensure a fair comparison with the classical EWMA, LH is calibrated to match a nominal in‐control average run length (ARL0) under normality for each smoothing parameter λ. The Monte Carlo studies across Normal, heavy–tailed t with four degrees of the freedom, and skewed Gamma Inputs show that, once they calibrated at Normality, the Haar mean channel typically exhibits smaller departures of ARL 0 from the 370 target under non–Normality and shorter out–of–control run lengths (ARL 1 ) for the mean shifts, relative to the classical EWMA with the same nominal false–alarm rate. These findings indicate that Haar‐EWMA provides a practical and interpretable robustness advantage while preserving the familiar implementation workflow of conventional EWMA monitoring. A focused isolated‐spike experiment shows that the detail‐sentinel flag rate rises from 20.39% at 3σ to 90.31% at 6σ, quantifying its diagnostic response to spike‐like observations.

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