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Homogeneously Weighted Moving Average Control Charts: Overview, Controversies, and New Directions

Author

Listed:
  • Jean-Claude Malela-Majika

    (Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Hatfield, Pretoria 0028, South Africa)

  • Schalk William Human

    (Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Hatfield, Pretoria 0028, South Africa)

  • Kashinath Chatterjee

    (Department of Biostatistics and Data Science, Augusta University, Augusta, GA 30912, USA)

Abstract

The homogeneously weighted moving average (HWMA) chart is a recent control chart that has attracted the attention of many researchers in statistical process control (SPC). The HWMA statistic assigns a higher weight to the most recent sample, and the rest is divided equally between the previous samples. This weight structure makes the HWMA chart more sensitive to small shifts in the process parameters when running in zero-state mode. Many scholars have reported its superiority over the existing charts when the process runs in zero-state mode. However, several authors have criticized the HWMA chart by pointing out its poor performance in steady-state mode due to its weighting structure, which does not reportedly comply with the SPC standards. This paper reviews and discusses all research works on HWMA-related charts (i.e., 55 publications) and provides future research ideas and new directions.

Suggested Citation

  • Jean-Claude Malela-Majika & Schalk William Human & Kashinath Chatterjee, 2024. "Homogeneously Weighted Moving Average Control Charts: Overview, Controversies, and New Directions," Mathematics, MDPI, vol. 12(5), pages 1-30, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:637-:d:1343252
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    References listed on IDEAS

    as
    1. Hongying Zhang & Zahid Rasheed & Majid Khan & Jimmy Joseph Namangale & Syed Masroor Anwar & Aamir Hamid & Tahir Mehmood, 2022. "A Distribution-Free THWMA Control Chart under Ranked Set Sampling," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-20, August.
    2. Shey-Huei Sheu & Yu-Tai Hsieh, 2009. "The extended GWMA control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 135-147.
    3. Zahid Rasheed & Majid Khan & Nafiu Lukman Abiodun & Syed Masroor Anwar & G. Khalaf & Saddam Akber Abbasi & Adrian Neagu, 2022. "Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-15, June.
    4. Tianhua Wang & Shuguang Huang, 2016. "An adaptive multivariate CUSUM control chart for signaling a range of location shifts," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(16), pages 4673-4691, August.
    5. Jimoh Olawale Ajadi & Muhammad Riaz, 2017. "Mixed multivariate EWMA-CUSUM control charts for an improved process monitoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6980-6993, July.
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