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The Dynamic Window Approach as a Tool to Improve Performance of Nonparametric Self-Starting Control Charts

Author

Listed:
  • Claudio Giovanni Borroni

    (Department of Statistics and Quantitative Methods, University of Milano-Bicocca, 20126 Milan, Italy
    These authors contributed equally to this work.)

  • Manuela Cazzaro

    (Department of Statistics and Quantitative Methods, University of Milano-Bicocca, 20126 Milan, Italy
    These authors contributed equally to this work.)

  • Paola Maddalena Chiodini

    (Department of Statistics and Quantitative Methods, University of Milano-Bicocca, 20126 Milan, Italy
    These authors contributed equally to this work.)

Abstract

The change-point model is an established methodology for the construction of self-starting control charts. Change-point charts are often nonparametric in order to be independent from any specific assumptions about the process distribution. Nonetheless, this methodology is usually implemented by considering all possible splits of a given stream of observations into two adjacent sub-samples. This can make the recent observations too influential and the chart’s signals too dependent on limited evidence. This paper proposes to correct such a distortion by using a window approach, which forces the use of only comparisons based on sub-samples of the same size. The resulting charts are “omnibus”, with respect to their having any kind of shift and also any direction of such shifts. To prove this, this paper focuses on a chart based on the Cramér–von Mises test. We report a simulation study evaluating the average number of readings to obtain a signal after a known shift has occurred. We conclude that, beyond being stable with respect to the direction of the shift, the new chart overcomes its competitors when the distribution heads toward regularity. Finally, the new approach is shown to have successful application to a real problem about air quality.

Suggested Citation

  • Claudio Giovanni Borroni & Manuela Cazzaro & Paola Maddalena Chiodini, 2025. "The Dynamic Window Approach as a Tool to Improve Performance of Nonparametric Self-Starting Control Charts," Mathematics, MDPI, vol. 13(6), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:938-:d:1610547
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    References listed on IDEAS

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    1. Shiwang Hou & Keming Yu, 2021. "A non-parametric CUSUM control chart for process distribution change detection and change type diagnosis," International Journal of Production Research, Taylor & Francis Journals, vol. 59(4), pages 1166-1186, February.
    2. Jong-Min Kim & Ning Wang & Yumin Liu, 2020. "Multi-Stage Change Point Detection with Copula Conditional Distribution with PCA and Functional PCA," Mathematics, MDPI, vol. 8(10), pages 1-23, October.
    3. Khanittha Talordphop & Yupaporn Areepong & Saowanit Sukparungsee, 2023. "Design and Analysis of Extended Exponentially Weighted Moving Average Signed-Rank Control Charts for Monitoring the Process Mean," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    4. Saber Ali & Zameer Abbas & Hafiz Zafar Nazir & Muhammad Riaz & Xingfa Zhang & Yuan Li, 2020. "On Designing Non-Parametric EWMA Sign Chart under Ranked Set Sampling Scheme with Application to Industrial Process," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    5. Jin Zhang, 2002. "Powerful goodness‐of‐fit tests based on the likelihood ratio," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 281-294, May.
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