A Novel Moving Average–Exponentiated Exponentially Weighted Moving Average (MA-Exp-EWMA) Control Chart for Detecting Small Shifts

Jun-Hao Lu and Chang-Yun Lin ()
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Jun-Hao Lu: Department of Applied Mathematics, Institute of Statistics, National Chung Hsing University, Taichung 40227, Taiwan
Chang-Yun Lin: Department of Applied Mathematics, Institute of Statistics, National Chung Hsing University, Taichung 40227, Taiwan

Mathematics, 2025, vol. 13, issue 18, 1-31

Abstract: Process monitoring plays a vital role in ensuring quality stability, and, operational efficiency across fields such as manufacturing, finance, biomedical science, and environmental monitoring. Among statistical tools, control charts are widely adopted for detecting variability and abnormal patterns. Since the introduction of the basic X-bar control chart by Shewhart in the 1920s, various improved methods have emerged to address the challenge of identifying small and latent process shifts, including CUSUM, MA, EWMA, and Exp-EWMA control charts. This study introduces a novel control chart—the Moving Average–Exponentiated Exponentially Weighted Moving Average (MA-Exp-EWMA) control chart—combining the smoothing effect of MA and the adaptive weighting of Exp-EWMA. Its goal is to improve the detection of small shifts and gradual changes. Performance is evaluated using average run length ( ARL ), standard deviation of run length ( SDRL ), and median run length ( MRL ). Monte Carlo simulations under different distributions (normal, exponential, gamma, and Student’s t ) and parameter settings assess the control chart’s sensitivity under various shift scenarios. Comparisons with existing control charts and an application to real data demonstrate the practical effectiveness of the proposed method in detecting small shifts.

Keywords: average run length; standard deviation of run length; median run length; MA control chart; EWMA control chart; Exp-EWMA control chart (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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