Adaptive Robust EWMA Control Chart for Monitoring Mean Shifts under Contaminated and Heavy-Tailed Processes
Abstract
Exponentially Weighted Moving Average (EWMA) control charts are widely employed in statistical process control to efficiently detect small and moderate shifts in the process mean. But classical EWMA models are heavily subject to normality assumptions and are very sensitive to outliers and even mild contamination in the in-control process that may lead to serious false alarm inflation and unpredictable run-length behavior. In this paper, we propose an adaptive robust EWMA control chart that can maintain stable false alarm performance under contaminated and heavy-tailed distributions. The proposed scheme uses the raw observations of EWMA recursion as a bounded robust score function with an online robust scale estimator to adjust control limits. This data-driven design ensures an approximate consistency of the in-control average run length at various levels of contamination and tail behavior. Simulations have demonstrated that the proposed chart exceeds classical and non-adaptive robust EWMA charts in terms of stability of false alarms and detection efficiency under heavy-tailed and contaminated baselines. The results indicate that the proposed adaptive robust EWMA chart is a robust and practical monitoring tool for industrial processes today with non-ideal data conditions.
References
- Ali, T. H., Taha, H. H., Sedeeq, B. S., & Hayawi, H. A. (2025). An innovative hybrid control chart combining wavelet decomposition and support vector machine for effective outlier detection. Frontiers in Applied Mathematics and Statistics, 11, 1682448. https://doi.org/10.3389/fams.2025.1682448.
- Borror, C. M., Montgomery, D. C., & Runger, G. C. (1999). Robustness of the EWMA control chart to non-normality. Journal of Quality Technology, 31(3), 309–316.
- Crowder, S. V. (1989). Design of exponentially weighted moving average schemes. Journal of Quality Technology, 21(3), 155–162.
- Gan, F. F. (1998). An optimal design of EWMA control charts based on median. Journal of Statistical Computation and Simulation, 61(1–2), 1–17.
- Gan, F. F. (2004). Monitoring observations generated from a linear process using EWMA charts. Journal of Statistical Computation and Simulation, 74(6), 425–436.
- Graham, M. A., Mukherjee, A., & Chakraborti, S. (2012). Distribution-free exponentially weighted moving average control charts for monitoring unknown location. Computational Statistics & Data Analysis, 56(8), 2535–2550.
- Graham, M. A., Mukherjee, A., & Chakraborti, S. (2012). Distribution-free exponentially weighted moving average control charts. Sequential Analysis, 31(4), 471–493.
- Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley.
- Hawkins, D. M., & Qiu, P. (2003). The changepoint model for statistical process control. Journal of Quality Technology, 35(4), 355–366.
- Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.
- Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). A multivariate exponentially weighted moving average control chart. Technometrics, 34(1), 46–53.
- Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics, 32(1), 1–12.
- M Taher, M., Al-Hasso, T. A. A.-R. S., & Ali, T. H. (2025). Comparative Evaluation of Classical Robust and Wavelet Enhanced Beta Regression Models for Proportional Data. Statistics, Optimization & Information Computing, 15(1), 324–335. https://doi.org/10.19139/soic-2310-5070-3144.
- Mahmoud, M. A., & Woodall, W. H. (2010). An evaluation of the robustness of EWMA control charts to non-normality. Communications in Statistics—Simulation and Computation, 39(1), 1–14.
- Montgomery, D. C. (2020). Introduction to Statistical Quality Control (8th ed.). Wiley.
- Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(3), 239–250.
- Taha Hussein Ali, Lazgeen Ramadhan, D., & Sarbast Saeed Ismael. (2026). Hybrid Robust Beta Regression Based on Support Vector Machines and Iterative Reweighted Least Squares. Statistics, Optimization & Information Computing, 15(3), 1513–1527. DOI:10.19139/soic-2310-5070-2850.
