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On the Efficient Monitoring of Multivariate Processes with Unknown Parameters

Author

Listed:
  • Nasir Abbas

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

  • Muhammad Riaz

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

  • Shabbir Ahmad

    (Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 45550, Pakistan)

  • Muhammad Abid

    (Department of Statistics, Government College University Faisalabad, Punjab 38000, Pakistan)

  • Babar Zaman

    (Department of Mathematical Sciences, Universiti Teknologi Malaysia, Skudai 81310, Malaysia)

Abstract

Control charts are commonly used tools that deal with monitoring of process parameters in an efficient manner. Multivariate control charts are more practical and are of greater importance for timely detection of assignable causes in multiple quality characteristics. This study deals with multivariate memory control charts to address smaller shifts in process mean vector. By adopting a new homogeneous weighting scheme, we have designed an efficient structure for multivariate process monitoring. We have also investigated the effect of an estimated variance covariance matrix on the proposed chart by considering different numbers and sizes of subgroups. We have evaluated the performance of the newly proposed multivariate chart under different numbers of quality characteristics and varying sample sizes. The performance measures used in this study include average run length, standard deviation run length, extra quadratic loss, and relative average run length. The performance analysis revealed that the proposed control chart outperforms the usual scheme under both known and estimated parameters. An application of the study proposal is also presented using a data set related to Olympic archery, for the monitoring of the location of arrows over the concentric rings on the archery board.

Suggested Citation

  • Nasir Abbas & Muhammad Riaz & Shabbir Ahmad & Muhammad Abid & Babar Zaman, 2020. "On the Efficient Monitoring of Multivariate Processes with Unknown Parameters," Mathematics, MDPI, vol. 8(5), pages 1-32, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:823-:d:360068
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    References listed on IDEAS

    as
    1. Ou, Yanjing & Wu, Zhang & Tsung, Fugee, 2012. "A comparison study of effectiveness and robustness of control charts for monitoring process mean," International Journal of Production Economics, Elsevier, vol. 135(1), pages 479-490.
    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. Willem Albers & Wilbert C.M. Kallenberg, 2004. "Estimation in Shewhart control charts: effects and corrections," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(3), pages 207-234, June.
    4. Bersimis, Sotiris & Panaretos, John & Psarakis, Stelios, 2005. "Multivariate Statistical Process Control Charts and the Problem of Interpretation: A Short Overview and Some Applications in Industry," MPRA Paper 6397, University Library of Munich, Germany.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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