Enhancing Process Monitoring with Robust EWMA Control Charts: A Study on Contaminated and Skewed Data

• Department of Statistics and Operation Research,
  University of Malta, Malta [derya.karagoz@um.edu.mt]

1 Abstract

This study investigates the performance of robust Exponentially Weighted Moving Average (EWMA) control charts, specifically the robust EWMA, robust weighted variance EWMA, and robust standard deviation EWMA charts, in monitoring contaminated and skewed statistical processes. To accommodate the asymmetric nature of the data, control limits are constructed using robust estimators such as the Winsorized mean and interquartile range (IQR).

A comprehensive comparison between the performance of classical EWMA and robust EWMA control charts is conducted using Monte Carlo simulations. The simulated datasets are generated to represent contaminated and skewed processes, derived from lognormal, gamma, and Weibull distributions with varying levels of skewness and contamination. Contamination models are employed to introduce outliers and other anomalies, while different smoothing parameters are applied to assess their influence on chart performance.

The evaluation focuses on Type I error rates, measuring the ability of the control charts to correctly detect whether the process remains in control. The results from the simulation study reveal that robust control charts significantly outperform their classical counterparts under contaminated and skewed conditions. These robust charts demonstrate improved sensitivity and reliability, making them suitable tools for monitoring non-normal processes in practical quality control applications.

By addressing the challenges posed by contamination and asymmetry in statistical processes, this work contributes to the advancement of robust process monitoring methodologies, offering practitioners effective solutions for maintaining quality in complex and irregular data environments.