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An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector

Author

Listed:
  • Muhammad Riaz

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

  • Babar Zaman

    (Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin 39524, Saudi Arabia)

  • Ishaq Adeyanju Raji

    (Dammam Community College, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • M. Hafidz Omar

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

  • Rashid Mehmood

    (Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin 39524, Saudi Arabia)

  • Nasir Abbas

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

Abstract

The special causes of variations, which is also known as a shift, can occur in a single or more than one related process characteristics. Statistical process control tools such as control charts are useful to monitor shifts in the process parameters (location and/or dispersion). In real-life situation, the shift is emerging in different sizes, and it is hard to identify it with classical control charts. Moreover, more than one process of characteristics required special attention because they must monitor jointly due to the association among them. This study offers two adaptive control charts to monitor the different sizes of a shift in the process mean vector. The novelty behind this study is to use dimensionally reduction techniques such as principal component analysis (PCA) and an adaptive method such as Huber and Bi-square functions. In brief, the multivariate cumulative sum control chart based on PCA is designed, and its plotting statistic is utilized as an input in the classical exponentially weighted moving average (EWMA) control chart. The run length (RL) properties of the proposed and other control charts are obtained by designing algorithms in MATLAB through a Monte Carlo simulation. For a single shift, the performance of the control charts is assessed through an average of RL, standard deviation of RL, and standard error of RL. Likewise, overall performance measures such as extra quadratic loss, relative ARL, and the performance comparison index are also used. The comparison reveals the superiority over other control charts. Furthermore, to emphasize the application process and benefits of the proposed control charts, a real-life example of the wind turbine process is included.

Suggested Citation

  • Muhammad Riaz & Babar Zaman & Ishaq Adeyanju Raji & M. Hafidz Omar & Rashid Mehmood & Nasir Abbas, 2022. "An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector," Mathematics, MDPI, vol. 10(12), pages 1-27, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2025-:d:836640
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    References listed on IDEAS

    as
    1. Ou, Yanjing & Wu, Zhang & Goh, Thong Ngee, 2011. "A new SPRT chart for monitoring process mean and variance," International Journal of Production Economics, Elsevier, vol. 132(2), pages 303-314, August.
    2. 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.
    3. Luo, Yunzhao & Li, Zhonghua & Wang, Zhaojun, 2009. "Adaptive CUSUM control chart with variable sampling intervals," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2693-2701, May.
    4. Zhang Wu & Jianxin Jiao & Mei Yang & Ying Liu & Zhaojun Wang, 2009. "An enhanced adaptive CUSUM control chart," IISE Transactions, Taylor & Francis Journals, vol. 41(7), pages 642-653.
    5. Yacine Aït-Sahalia & Dacheng Xiu, 2019. "Principal Component Analysis of High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 287-303, January.
    6. Petros E. Maravelakis, 2012. "Measurement error effect on the CUSUM control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 323-336, May.
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