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Cumulative Sum Chart Modeled under the Presence of Outliers

Author

Listed:
  • Nasir Abbas

    (Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Mu’azu Ramat Abujiya

    (Preparatory Year Mathematics Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Muhammad Riaz

    (Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Tahir Mahmood

    (Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China)

Abstract

Cumulative sum control charts that are based on the estimated control limits are extensively used in practice. Such control limits are often characterized by a Phase I estimation error. The presence of these errors can cause a change in the location and/or width of control limits resulting in a deprived performance of the control chart. In this study, we introduce a non-parametric Tukey’s outlier detection model in the design structure of a two-sided cumulative sum (CUSUM) chart with estimated parameters for process monitoring. Using Monte Carlo simulations, we studied the estimation effect on the performance of the CUSUM chart in terms of the average run length and the standard deviation of the run length. We found the new design structure is more stable in the presence of outliers and requires fewer amounts of Phase I observations to stabilize the run-length performance. Finally, a numerical example and practical application of the proposed scheme are demonstrated using a dataset from healthcare surveillance where received signal strength of individuals’ movement is the variable of interest. The implementation of classical CUSUM shows that a shift detection in Phase II that received signal strength data is indeed masked/delayed if there are outliers in Phase I data. On the contrary, the proposed chart omits the Phase I outliers and gives a timely signal in Phase II.

Suggested Citation

  • Nasir Abbas & Mu’azu Ramat Abujiya & Muhammad Riaz & Tahir Mahmood, 2020. "Cumulative Sum Chart Modeled under the Presence of Outliers," Mathematics, MDPI, vol. 8(2), pages 1-30, February.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:269-:d:322045
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    References listed on IDEAS

    as
    1. Asma Amdouni & Philippe Castagliola & Hassen Taleb & Giovanni Celano, 2017. "A variable sampling interval Shewhart control chart for monitoring the coefficient of variation in short production runs," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5521-5536, October.
    2. Mu’azu Ramat Abujiya & Muhammad Riaz & Muhammad Hisyam Lee, 2015. "Enhanced Cumulative Sum Charts for Monitoring Process Dispersion," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-22, April.
    3. Teoh, W.L. & Khoo, Michael B.C. & Castagliola, Philippe & Yeong, W.C. & Teh, S.Y., 2017. "Run-sum control charts for monitoring the coefficient of variation," European Journal of Operational Research, Elsevier, vol. 257(1), pages 144-158.
    4. Hubert, Mia & Dierckx, Goedele & Vanpaemel, Dina, 2013. "Detecting influential data points for the Hill estimator in Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 13-28.
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