Univariate and data-depth based multivariate control charts using trimmed mean and winsorized standard deviation

TL;DR

This paper introduces robust multivariate control charts based on trimmed means and winsorized variances, improving robustness and efficiency over traditional Shewhart charts, with theoretical analysis and simulation validation.

Contribution

It proposes a novel robust control chart methodology using data-depth functions, extending Shewhart charts with improved statistical properties and applicability to multivariate data.

Findings

Robust control charts outperform traditional ones in simulations.

The proposed method maintains efficiency under various data distributions.

Theoretical properties support the robustness of the new statistics.

Abstract

Over the years, the most popularly used control chart for statistical process control has been Shewhart's $\bar{X}-S$ or $\bar{X}-R$ chart along with its multivariate generalizations. But, such control charts suffer from the lack of robustness. In this paper, we propose a modified and improved version of Shewhart chart, based on trimmed mean and winsorized variance that proves robust and more efficient. We have generalized this approach of ours with suitable modifications using depth functions for Multivariate control charts and EWMA charts as well. We have discussed the theoretical properties of our proposed statistics and have shown the efficiency of our methodology on univariate and multivariate simulated datasets. We have also compared our approach to the other popular alternatives to Shewhart Chart already proposed and established the efficacy of our methodology.