IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1126-d1078643.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1126/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1126/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Amer Ibrahim Al-Omari & Abdul Haq, 2012. "Improved quality control charts for monitoring the process mean, using double-ranked set sampling methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 745-763, August.
    2. Zhenlin Yang & Min Xie, 2000. "Process monitoring of exponentially distributed characteristics through an optimal normalizing transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(8), pages 1051-1063.
    3. Al-Omari Amer Ibrahim & Al-Nasser Amjad D., 2011. "Statistical Quality Control Limits for the Sample Mean Chart Using Robust Extreme Ranked Set Sampling," Stochastics and Quality Control, De Gruyter, vol. 26(1), pages 73-89, January.
    4. Lai K. Chan & Heng J. Cui, 2003. "Skewness correction X̄ and R charts for skewed distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 555-573, September.
    5. 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.
    6. 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.
    7. Abdul Haq & Amer Al-Omari, 2015. "A new Shewhart control chart for monitoring process mean based on partially ordered judgment subset sampling," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1185-1202, May.
    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. Abdul Haq & Amer Al-Omari, 2015. "A new Shewhart control chart for monitoring process mean based on partially ordered judgment subset sampling," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1185-1202, May.
    2. Jing Jia Zhou & Kok Haur Ng & Kooi Huat Ng & Shelton Peiris & You Beng Koh, 2022. "Asymmetric Control Limits for Weighted-Variance Mean Control Chart with Different Scale Estimators under Weibull Distributed Process," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    3. Shih-Chou Kao & Chuan-Ching Ho & Ying-Chin Ho, 2006. "Transforming the exponential by minimizing the sum of the absolute differences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(7), pages 691-702.
    4. Pandu R. Tadikamalla & Dana G. Popescu, 2007. "Kurtosis correction method for X̄ and R control charts for long‐tailed symmetrical distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 371-383, June.
    5. Nandini Das, 2011. "Control Charts Based on the g-and-h Distribution," Stochastics and Quality Control, De Gruyter, vol. 26(1), pages 3-14, January.
    6. Shih-Chou Kao, 2010. "Normalization of the origin-shifted exponential distribution for control chart construction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1067-1087.
    7. Shih-Chou Kao & Chuanching Ho, 2007. "Monitoring a Process of Exponentially Distributed Characteristics through Minimizing the Sum of the Squared Differences," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(1), pages 137-149, February.
    8. Muhammad Abid & Hafiz Zafar Nazir & Muhammad Tahir & Muhammad Riaz, 2018. "On designing a new cumulative sum Wilcoxon signed rank chart for monitoring process location," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-18, April.
    9. Shidong Wu & Hengrui Ma & Abdullah M. Alharbi & Bo Wang & Li Xiong & Suxun Zhu & Lidong Qin & Gangfei Wang, 2023. "Integrated Energy System Based on Isolation Forest and Dynamic Orbit Multivariate Load Forecasting," Sustainability, MDPI, vol. 15(20), pages 1-23, October.

    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:11:y:2023:i:5:p:1126-:d:1078643. 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.