IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i21p2772-d669988.html
   My bibliography  Save this article

Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

Author

Listed:
  • Ishaq Adeyanju Raji

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

  • 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)

Abstract

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling T 2 chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes.

Suggested Citation

  • Ishaq Adeyanju Raji & Nasir Abbas & Mu’azu Ramat Abujiya & Muhammad Riaz, 2021. "Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection," Mathematics, MDPI, vol. 9(21), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2772-:d:669988
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/21/2772/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/21/2772/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hang Zhang & Susan Albin, 2009. "Detecting outliers in complex profiles using a χ control chart method," IISE Transactions, Taylor & Francis Journals, vol. 41(4), pages 335-345.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Moura Neto, F. & Souza, P. & de Magalhães, M.S., 2019. "Determining baseline profile by diffusion maps," European Journal of Operational Research, Elsevier, vol. 279(1), pages 107-123.
    2. Fabbri, Ricardo & Bastos, Ivan N. & Neto, Francisco D. Moura & Lopes, Francisco J.P. & Gonçalves, Wesley N. & Bruno, Odemir M., 2014. "Multi-q pattern classification of polarization curves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 332-339.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2772-:d:669988. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.