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Deviance and Pearson Residuals-Based Control Charts with Different Link Functions for Monitoring Logistic Regression Profiles: An Application to COVID-19 Data

Author

Listed:
  • Maryam Cheema

    (Department of Statistics, University of Sargodha, Sargodha 40100, Pakistan)

  • Muhammad Amin

    (Department of Statistics, University of Sargodha, Sargodha 40100, Pakistan)

  • Tahir Mahmood

    (Industrial and Systems Engineering Department, College of Computing and Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
    Interdisciplinary Research Centre for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Muhammad Faisal

    (Faculty of Health Studies, University of Bradford, Bradford BD7 1DP, UK)

  • Kamel Brahim

    (Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia)

  • Ahmed Elhassanein

    (Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia)

Abstract

In statistical process control, the control charts are an effective tool to monitor the process. When the process is examined based on an exponential family distributed response variable along with a single explanatory variable, the generalized linear model (GLM) provides better estimates and GLM-based charts are preferred. This study is designed to propose GLM-based control charts using different link functions (i.e., logit, probit, c-log-log, and cauchit) with the binary response variable. The Pearson residuals (PR)- and deviance residuals (DR)-based control charts for logistic regression are proposed under different link functions. For evaluation purposes, a simulation study is designed to evaluate the performance of the proposed control charts. The results are compared based on the average run length (ARL). Moreover, the proposed charts are implemented on a real application for COVID-19 death monitoring. The Monte Carlo simulation study and real applications show that the performance of the model-based control charts with the c-log-log link function gives a better performance as compared to model-based control charts with other link functions.

Suggested Citation

  • Maryam Cheema & Muhammad Amin & Tahir Mahmood & Muhammad Faisal & Kamel Brahim & Ahmed Elhassanein, 2023. "Deviance and Pearson Residuals-Based Control Charts with Different Link Functions for Monitoring Logistic Regression Profiles: An Application to COVID-19 Data," Mathematics, MDPI, vol. 11(5), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1113-:d:1077682
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    References listed on IDEAS

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    1. Kasra Jahani & Hamidreza Feili & Fereydon Ohadi, 2019. "Phase II monitoring of the nominal logistic regression profiles based on Wald and Rao score test statistics (a case study in healthcare: diabetic patients)," International Journal of Productivity and Quality Management, Inderscience Enterprises Ltd, vol. 27(2), pages 161-176.
    2. Paria Soleimani & Shervin Asadzadeh, 2022. "Effect of non-normality on the monitoring of simple linear profiles in two-stage processes: a remedial measure for gamma-distributed responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(11), pages 2870-2890, August.
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    Cited by:

    1. Wen Zhang & Xiaofeng Xu & Jun Wu & Kaijian He, 2023. "Preface to the Special Issue on “Computational and Mathematical Methods in Information Science and Engineering”," Mathematics, MDPI, vol. 11(14), pages 1-4, July.

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