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Data-Driven Surveillance of Internet Usage Using a Polynomial Profile Monitoring Scheme

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Listed:
  • Unarine Netshiozwi

    (Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa)

  • Ali Yeganeh

    (Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa)

  • Sandile Charles Shongwe

    (Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa)

  • Ahmad Hakimi

    (Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj 0098, Iran)

Abstract

Control charts, which are one of the major tools in the Statistical Process Control (SPC) domain, are used to monitor a process over time and improve the final quality of a product through variation reduction and defect prevention. As a novel development of control charts, referred to as profile monitoring, the study variable is not defined as a quality characteristic; it is a functional relationship between some explanatory and response variables which are monitored in such a way that the major aim is to check the stability of this model (profile) over time. Most of the previous works in the area of profile monitoring have focused on the development of different theories and assumptions, but very little attention has been paid to the practical application in real-life scenarios in this field of study. To address this knowledge gap, this paper proposes a monitoring framework based on the idea of profile monitoring as a data-driven method to monitor the internet usage of a telecom company. By definition of a polynomial model between the hours of each day and the internet usage within each hour, we propose a framework with three monitoring goals: (i) detection of unnatural patterns, (ii) identifying the impact of policies such as providing discounts and, (iii) investigation of general social behaviour variations in the internet usage. The results shows that shifts of different magnitudes can occur in each goal. With the aim of different charting statistics such as Hoteling T 2 and MEWMA, the proposed framework can be properly implemented as a monitoring scheme under different shift magnitudes. The results indicate that the MEWMA scheme can perform well in small shifts and has faster detection ability as compared to the Hoteling T 2 scheme.

Suggested Citation

  • Unarine Netshiozwi & Ali Yeganeh & Sandile Charles Shongwe & Ahmad Hakimi, 2023. "Data-Driven Surveillance of Internet Usage Using a Polynomial Profile Monitoring Scheme," Mathematics, MDPI, vol. 11(17), pages 1-23, August.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3650-:d:1223623
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    References listed on IDEAS

    as
    1. Han, Dong & Tsung, Fugee, 2006. "A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 368-386, March.
    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. Arthur Yeh & Longcheen Huwang & Yu-Mei Li, 2009. "Profile monitoring for a binary response," IISE Transactions, Taylor & Francis Journals, vol. 41(11), pages 931-941.
    4. Barbeito, Inés & Zaragoza, Sonia & Tarrío-Saavedra, Javier & Naya, Salvador, 2017. "Assessing thermal comfort and energy efficiency in buildings by statistical quality control for autocorrelated data," Applied Energy, Elsevier, vol. 190(C), pages 1-17.
    5. Dong Ding & Fugee Tsung & Jian Li, 2017. "Ordinal profile monitoring with random explanatory variables," International Journal of Production Research, Taylor & Francis Journals, vol. 55(3), pages 736-749, February.
    6. Mithun Ghosh & Yongxiang Li & Li Zeng & Zijun Zhang & Qiang Zhou, 2021. "Modeling multivariate profiles using Gaussian process-controlled B-splines," IISE Transactions, Taylor & Francis Journals, vol. 53(7), pages 787-798, April.
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