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Sustainability
Volume 15
Issue 8
10.3390/su15086675
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Article

Monitoring of Location Parameters with a Measurement Error under the Bayesian Approach Using Ranked-Based Sampling Designs with Applications in Industrial Engineering

by
Imad Khan
1,
Muhammad Noor-ul-Amin
2,
Dost Muhammad Khan
1,
Salman A. AlQahtani
3,*,
Mostafa Dahshan
4 and
Umair Khalil
1
1
Department of Statistics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
2
Department of Statistics, COMSATS University Islamabad Lahore Campus, Lahore 54000, Pakistan
3
Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, P.O. Box 51178, Riyadh 11543, Saudi Arabia
4
School of Computing, Mathematics, and Engineering, Charles Sturt University, Panorama Avenue, Bathurst, NSW 2795, Australia
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(8), 6675; https://doi.org/10.3390/su15086675
Submission received: 23 February 2023 / Revised: 27 March 2023 / Accepted: 29 March 2023 / Published: 14 April 2023
(This article belongs to the Special Issue A Multidisciplinary Approach to Sustainability)
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Abstract

To detect sustainable changes in the production processes, memory-type control charts are frequently utilized. This study is conducted to assess the performance of the Bayesian adaptive exponentially weighted moving average (AEWMA) control chart using ranked set sampling schemes following two different loss functions in the presence of a measurement error for posterior and posterior predictive distributions using conjugate priors. This study is based on the covariate model and multiple measurement methods in the presence of a measurement error (ME). The performance of the proposed Bayesian-AEWMA control chart with ME has been evaluated through the average run length and the standard deviation of the run length. Finally, a real-life application in semiconductor manufacturing was conducted to evaluate the effectiveness of the proposed Bayesian-AEWMA control chart with a measurement error based on different ranked set sampling schemes. The results demonstrate that the proposed control chart, in the presence of a measurement error, performed well in detecting out-of-control signals compared to the existing control chart. However, the median ranked set sampling scheme (MRSS) proved to be better than the other two schemes in the presence of a measurement error.
Keywords: Bayesian approach; loss function; AEWMA; measurement error; average run length; control charts Bayesian approach; loss function; AEWMA; measurement error; average run length; control charts

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MDPI and ACS Style

Khan, I.; Noor-ul-Amin, M.; Khan, D.M.; AlQahtani, S.A.; Dahshan, M.; Khalil, U. Monitoring of Location Parameters with a Measurement Error under the Bayesian Approach Using Ranked-Based Sampling Designs with Applications in Industrial Engineering. Sustainability 2023, 15, 6675. https://doi.org/10.3390/su15086675

AMA Style

Khan I, Noor-ul-Amin M, Khan DM, AlQahtani SA, Dahshan M, Khalil U. Monitoring of Location Parameters with a Measurement Error under the Bayesian Approach Using Ranked-Based Sampling Designs with Applications in Industrial Engineering. Sustainability. 2023; 15(8):6675. https://doi.org/10.3390/su15086675

Chicago/Turabian Style

Khan, Imad, Muhammad Noor-ul-Amin, Dost Muhammad Khan, Salman A. AlQahtani, Mostafa Dahshan, and Umair Khalil. 2023. "Monitoring of Location Parameters with a Measurement Error under the Bayesian Approach Using Ranked-Based Sampling Designs with Applications in Industrial Engineering" Sustainability 15, no. 8: 6675. https://doi.org/10.3390/su15086675

APA Style

Khan, I., Noor-ul-Amin, M., Khan, D. M., AlQahtani, S. A., Dahshan, M., & Khalil, U. (2023). Monitoring of Location Parameters with a Measurement Error under the Bayesian Approach Using Ranked-Based Sampling Designs with Applications in Industrial Engineering. Sustainability, 15(8), 6675. https://doi.org/10.3390/su15086675

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