Robust adaptive EWMA–CUSUM control charts for monitoring autocorrelated and non-normal processes

Abstract

Control charts are widely used for monitoring process stability; however, their performance deteriorates when observations exhibit both autocorrelation and non-normality. This study proposes a Robust Adaptive EWMA–CUSUM (RAEC) control chart that integrates robust location and scale estimation with an adaptive EWMA–CUSUM model in which the shift estimate is updated dynamically according to recent process behavior, thereby improving responsiveness to evolving process changes while maintaining robustness to outliers and distributional departures from normality. The performance of the proposed chart was evaluated through extensive Monte Carlo simulations under normal, heavy-tailed Student’s (t), skewed lognormal, and contaminated distributions, and was illustrated using 130 daily observations of the Kenya shilling overnight interbank average benchmark interest rate. Simulation results demonstrate that the proposed RAEC chart consistently achieves shorter out-of-control average run lengths than conventional EWMA, CUSUM, and existing hybrid monitoring schemes, particularly for small and moderate process shifts, while maintaining satisfactory in-control performance. The real-data application further illustrates the proposed method’s ability to identify emerging structural changes in an autocorrelated financial process. Although the empirical illustration is based on a single financial time series, the proposed framework provides a flexible and robust monitoring strategy that can be extended to a broader range of industrial, financial, and environmental applications, with future validation on larger and more diverse datasets.

Keywords

• Adaptive control charts
• autocorrelated processes
• CUSUM
• EWMA

Ethical Statement

Not Applicable

Thanks

The authors sincerely thank the students of the Quality Control and Sampling Inspection class at the University of Embu for their enthusiasm and active engagement throughout the course, which helped inspire key aspects of this research

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