Monitoring of manufacturing process using bayesian EWMA control chart under ranked based sampling designs

Imad Khan; Muhammad Noor-Ul-Amin; Dost Muhammad Khan; Emad A A Ismail; Wojciech Sumelka

doi:10.1038/s41598-023-45553-x

Monitoring of manufacturing process using bayesian EWMA control chart under ranked based sampling designs

Sci Rep. 2023 Oct 25;13(1):18240. doi: 10.1038/s41598-023-45553-x.

Authors

Imad Khan¹, Muhammad Noor-Ul-Amin², Dost Muhammad Khan¹, Emad A A Ismail³, Wojciech Sumelka⁴

Affiliations

¹ Department of Statistics, Abdul Wali Khan University Mardan, Mardan, Pakistan.
² COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan. nooramin.stats@gmail.com.
³ Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh, 11587, P.O. Box 71115, Saudi Arabia.
⁴ Institute of Structural Analysis, Poznan University of Technology, 60-965, Poznan, Poland. wojciech.sumelka@put.poznan.pl.

Abstract

Control charts, including exponentially moving average (EWMA) , are valuable for efficiently detecting small to moderate shifts. This study introduces a Bayesian EWMA control chart that employs ranked set sampling (RSS) with known prior information and two distinct loss functions (LFs), the Square Error Loss function (SELF) and the Linex Loss function (LLF), for posterior and posterior predictive distributions. The chart's performance is assessed using average run length (ARL) and standard deviation of run length (SDRL) profiles, and it is compared to the Bayesian EWMA control chart based on simple random sampling (SRS). The results indicate that the proposed control chart detects small to moderate shifts more effectively. The application in semiconductor manufacturing provides concrete evidence that the Bayesian EWMA control chart, when implemented with RSS schemes, demonstrates a higher degree of sensitivity in detecting deviations from normal process behavior. Comparison to the Bayesian EWMA control chart using SRS, it exhibits a superior ability to identify and flag instances where the manufacturing process is going out of control. This heightened sensitivity is critical for promptly addressing and rectifying issues, which ultimately contributes to improved quality control in semiconductor production.