A New Bayesian Control Chart for the Monitoring of Parametric Uncertainty
Tahir ABBAS, Muhammad ABID, Iffrah RASHEED
Abstract. Bayesian control charts have proven to be powerful statistical process control tools for monitoring manufacturing processes and controlling variability. Control charts in a Bayesian setup are particularly advantageous in situations where parameter uncertainty is unavoidable in industrial engineering. Memory-type control charts, such as EWMA, HWMA, and DEWMA, are designed under a Bayesian framework to handle parametric uncertainty. This study introduces a new Double HWMA (DHWMA_B) chart within the Bayesian framework to further enhance the detection potential of the DHWMA chart. The Bayesian DHWMA chart is specifically designed to monitor the process mean and has effectively addressed the challenge of parametric uncertainty. The posterior estimates are obtained by carefully integrating prior knowledge with current information. The designed charts are evaluated using various performance measures of the run length (RL) profile, such as the average RL and the RL standard deviation. The RL characteristics of the proposed DHWMA_B and competing charts are computed and compared. The simulation study demonstrates that the DHWMA_B chart outperformed the competing charts in detecting the fault early. The proposal chart for DHWMA_B effectiveness shows effectiveness across all types of shifts in the process parameter. The real-world application in the aerospace manufacturing industry also demonstrates the superiority of the proposed DHWMA_B chart.
Keywords
Aerospace Manufacturing, Bayesian Charts, Posterior Distribution, Run Length Profiles, Statistical Process Control
Published online 5/10/2026, 6 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Tahir ABBAS, Muhammad ABID, Iffrah RASHEED, A New Bayesian Control Chart for the Monitoring of Parametric Uncertainty, Materials Research Proceedings, Vol. 66, pp 434-439, 2026
DOI: https://doi.org/10.21741/9781644904152-40
The article was published as article 40 of the book Advanced Materials and Sustainable Energy Technologies
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] Rakitzis, A. C., Castagliola, P., & Maravelakis, P. E. (2018). Cumulative sum control charts for monitoring geometrically inflated Poisson processes: An application to infectious disease counts data. Statistical Methods in Medical Research, 27(2), 622-641. https://doi.org/10.1177/0962280216641985
[2] Jones, C. L., Abdel‐Salam, A. S. G., & Mays, D. A. (2023). Novel Bayesian CUSUM and EWMA control charts via various loss functions for monitoring processes. Quality and Reliability Engineering International, 39(1), 164-189. https://doi.org/10.1002/qre.3229
[3] Khan, I., Noor-ul-Amin, M., Khan, D. M., Ismail, E. A., & Sumelka, W. (2023). Monitoring of manufacturing process using Bayesian EWMA control chart under ranked-based sampling designs. Scientific Reports, 13(1), 18240. https://doi.org/10.1038/s41598-023-45553-x
[4] Maravelakis, P. E. (2012). Measurement error effect on the CUSUM control chart. Journal of Applied Statistics, 39(2), 323-336. https://doi.org/10.1080/02664763.2011.590188
[5] Montgomery, D. C. (2009). Introduction to Statistical Quality Control. 6 ed., John Wiley & Sons.
[6] Noor-ul-Amin, M., Khan, I., Iqbal, J., Rasheed, Z., Ismail, E. A., & Ahmad, B. (2024). Memory type Max-EWMA control chart for the Weibull process under the Bayesian theory. Scientific Reports, 14(1), 3111. https://doi.org/10.1038/s41598-024-52109-0
[7] Page, E.S. (1954). Continuous inspection schemes. Biometrika 41, 100-115. https://doi.org/10.1093/biomet/41.1-2.100
[8] Roberts, S.W. (1959). Control chart tests based on geometric moving averages. Technometrics 1, 239-250. https://doi.org/10.1080/00401706.1959.10489860
[9] Shewhart, W.A. (1931). Economic control of the quality of the manufactured product.
[10] Wang, K., & Tsung, F. (2022). Bayesian cross-product quality control via transfer learning. International Journal of Production Research, 60(3), 847-865. https://doi.org/10.1080/00207543.2020.1845413
