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The generally weighted moving average control chart for monitoring the process mean of autocorrelated observations

Author

Listed:
  • Wei-Teng Sheu

    (National Taiwan University of Science and Technology)

  • Shih-Hao Lu

    (National Taiwan University of Science and Technology)

  • Ying-Lin Hsu

    (National Chung Hsing University)

Abstract

The statistical process control chart is primarily applied to monitor the production process or service process and detect the process shifts as soon as possible. The EWMA (exponentially weighted moving average) control chart has been widely used to detect small shifts in the process mean. Sheu and Lin (Qual Eng 16:209–231, 2003) proposed the GWMA (generally weighted moving average) control chart, for detecting small process mean shifts of independent observations. The GWMA control chart is the extended version of EWMA control chart. The GWMA control chart has been widely investigated. In this paper, the definition, and properties of the GWMA control chart are being further analyzed and investigated for detecting small process mean shifts of autocorrelated observations. The weight of GWMA technique depends on time t. Thus, there is no recursive formula for the GWMA technique. The GWMA technique has no Markovian property. The GWMA control chart is more practical for detecting small process mean shifts of autocorrelated observations. A numerical simulation comparison shows that the GWMA control chart outperforms the EWMA control chart for detecting small process mean shifts of autocorrelated observations.

Suggested Citation

  • Wei-Teng Sheu & Shih-Hao Lu & Ying-Lin Hsu, 2025. "The generally weighted moving average control chart for monitoring the process mean of autocorrelated observations," Annals of Operations Research, Springer, vol. 349(1), pages 139-167, June.
    • Handle: RePEc:spr:annopr:v:349:y:2025:i:1:d:10.1007_s10479-023-05384-5
    DOI: 10.1007/s10479-023-05384-5
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    References listed on IDEAS

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    1. B L MacCarthy & T Wasusri, 2001. "Statistical process control for monitoring scheduling performance—addressing the problem of correlated data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(7), pages 810-820, July.
    2. Shey-Huei Sheu & Shin-Li Lu, 2008. "Monitoring Autocorrelated Process Mean And Variance Using A Gwma Chart Based On Residuals," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(06), pages 781-792.
    3. Shey‐Huei Sheu & William S. Griffith, 1996. "Optimal number of minimal repairs before replacement of a system subject to shocks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 319-333, April.
    4. Kashinath Chatterjee & Christos Koukouvinos & Angeliki Lappa, 2023. "Monitoring process mean and dispersion with one double generally weighted moving average control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 50(1), pages 19-42, January.
    5. A B Koehler & N B Marks & R T O'connell, 2001. "EWMA control charts for autoregressive processes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(6), pages 699-707, June.
    6. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 87-95, January.
    7. Yu-min Liu & Li Xue, 2015. "The optimization design of EWMA charts for monitoring environmental performance," Annals of Operations Research, Springer, vol. 228(1), pages 113-124, May.
    8. Mitra, Amitava & Lee, Kang Bok & Chakraborti, Subhabrata, 2019. "An adaptive exponentially weighted moving average-type control chart to monitor the process mean," European Journal of Operational Research, Elsevier, vol. 279(3), pages 902-911.
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