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<p>After accurately approximating the average in-control run length (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11009_2025_10155_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(ARL_0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mi>R</mi> <msub> <mi>L</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>) for a multivariate Exponential Weighted Moving Average (EWMA) chart, we explore the optimal design of the weight parameter to minimize the stationary average delay detection time (SADDT). We conduct numerical comparisons of SADDT between Moving Average (MA), Cumulative Sum (CUSUM), Generalized Likelihood Ratio Test (GLRT), and Shiryayev-Roberts (S-R) charts for a given <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11009_2025_10155_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(ARL_0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mi>R</mi> <msub> <mi>L</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>. Additionally, we propose hard-threshold and soft-threshold EWMA charts for detecting changes characterized by sparse signals, where the change occurs in only a few components. Comparative analyses, including adaptive techniques, demonstrate the robust performance and straightforward design of the EWMA procedure, making it a recommended choice. The detection of mean changes in daily returns for Dow Jones industrial stock prices is used for illustration.</p>

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Optimal Multivariate EWMA Chart for Detecting Common Change in Mean

  • 期刊论文

  • 发表日期：

    2025年3月24日

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  • Yanhong Wu,
  • Wei Biao Wu

摘要

After accurately approximating the average in-control run length ( \(ARL_0\) A R L 0 ) for a multivariate Exponential Weighted Moving Average (EWMA) chart, we explore the optimal design of the weight parameter to minimize the stationary average delay detection time (SADDT). We conduct numerical comparisons of SADDT between Moving Average (MA), Cumulative Sum (CUSUM), Generalized Likelihood Ratio Test (GLRT), and Shiryayev-Roberts (S-R) charts for a given \(ARL_0\) A R L 0 . Additionally, we propose hard-threshold and soft-threshold EWMA charts for detecting changes characterized by sparse signals, where the change occurs in only a few components. Comparative analyses, including adaptive techniques, demonstrate the robust performance and straightforward design of the EWMA procedure, making it a recommended choice. The detection of mean changes in daily returns for Dow Jones industrial stock prices is used for illustration.