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On Designing of Bayesian Shewhart-Type Control Charts for Maxwell Distributed Processes with Application of Boring Machine

Author

Listed:
  • Fatimah Alshahrani

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Ibrahim M. Almanjahie

    (Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia)

  • Majid Khan

    (Department of Statistics, Government Postgraduate College Haripur, Haripur 22620, Pakistan
    Department of Mathematics and Statistics, Riphah International University, Islamabad 46000, Pakistan)

  • Syed M. Anwar

    (Department of Statistics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan)

  • Zahid Rasheed

    (Department of Mathematics, Women University of Azad Jammu and Kashmir, Bagh 12500, Pakistan)

  • Ammara N. Cheema

    (Department of Mathematics, Air University Islamabad Pakistan, Islamabad 44000, Pakistan)

Abstract

The quality characteristic(s) are assumed to follow the normal distribution in many control chart constructions, although this assumption may not hold in some instances. This study proposes the Bayesian-I and Bayesian-II Shewhart-type control charts for monitoring the Maxwell scale parameter in the phase II study. The posterior and predictive distributions are used to construct the control limits for the proposed Bayesian-I and Bayesian-II Shewhart-type control charts, respectively. Various performance indicators, including average run length, quadratic loss, relative average run length, and performance comparison index, are utilized to evaluate the performance of the proposed control charts. The Bayesian-I and Bayesian-II Shewhart-type control charts are compared to their competitive CUSUM V , EWMA V and V control charts. Sensitivity analysis is also performed to study the effect of hyperparameter values on the performance behavior of the proposed control charts. Finally, real-life data is analyzed for the implementation of the proposed control charts.

Suggested Citation

  • Fatimah Alshahrani & Ibrahim M. Almanjahie & Majid Khan & Syed M. Anwar & Zahid Rasheed & Ammara N. Cheema, 2023. "On Designing of Bayesian Shewhart-Type Control Charts for Maxwell Distributed Processes with Application of Boring Machine," Mathematics, MDPI, vol. 11(5), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1126-:d:1078643
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    References listed on IDEAS

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    6. Muhammad Aslam & Syed Masroor Anwar, 2020. "An improved Bayesian Modified-EWMA location chart and its applications in mechanical and sport industry," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-19, February.
    7. Surria Noor & Muhammad Noor-ul-Amin & Muhammad Mohsin & Azaz Ahmed, 2022. "Hybrid exponentially weighted moving average control chart using Bayesian approach," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(12), pages 3960-3984, May.
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    Cited by:

    1. Wei Yang & Xueting Ji & Hongxing Cai & Jiujun Zhang, 2025. "Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing," Mathematics, MDPI, vol. 13(4), pages 1-29, February.
    2. Yadpirun Supharakonsakun, 2024. "Bayesian Control Chart for Number of Defects in Production Quality Control," Mathematics, MDPI, vol. 12(12), pages 1-10, June.

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