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

Fatimah Alshahrani, Ibrahim M. Almanjahie, Majid Khan (), Syed M. Anwar, Zahid Rasheed and Ammara N. Cheema
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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
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

Mathematics, 2023, vol. 11, issue 5, 1-20

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.

Keywords: hyperparameters; Maxwell distribution; performance measures; posterior predictive distribution; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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