EWMA control charts based on robust estimators: A powerful tool for monitoring a process with a non-normal distribution

Abstract

This paper presents a study on using memory-type control charts to detect small to moderate shifts in the process mean, particularly when the underlying distribution deviates from normal assumptions. To address this, robust estimators based on modified maximum likelihood estimation (MMLE) and Lloyd’s BLUE estimators using generalized least square estimation (GLSE) are proposed. The proposed estimators utilize auxiliary information to enhance sensitivity against abrupt changes in the mean. Additionally, they play a crucial role in refining the precision of the estimated mean, contributing to a more accurate and nuanced estimation of the true mean. The efficiency and robustness of these estimators are compared with conventional ones from the literature. The proposed robust estimators are integrated into the design of the exponentially weighted moving average (EWMA) control chart. Performance evaluation is based on average run lengths (ARLs), standard deviation, and percentiles of the run lengths. A real-life example illustrates the significance of the proposed estimators over conventional ones for non-normal distributions. The results demonstrate that the EWMA control chart with proposed estimators outperforms competitors in terms of ARLs, SDRLs, and percentiles. This study offers insights into using robust estimators to enhance memory-type control charts' performance for non-normal distributions.