A Robust L‐Comoments Covariance Matrix‐Based Hotelling's T2${T^{2}}$ Control Chart for Monitoring High‐Dimensional Non‐Normal Multivariate Data in the Presence of Outliers

ABSTRACT This article introduces a new robust multivariate Hotelling T‐square (TS) control chart that incorporates an L‐Comoments covariance matrix into a multivariate statistical process control (MSPC) charting scheme to enhance its robustness and detection ability. However, among the most popular, conventional Hotelling TS charts are affected by outliers and based on the so‐called classical covariance matrix estimators, which in turn presuppose normality and independence. This sensitivity reduces their usefulness in complicated practical problems where skewness, heavy tails, and outliers are likely to appear. Using L‐Comoments as a basis of the new chart can overcome these limitations since L‐Comoments are not affected by outliers. The performance of the proposed Hotelling TS (HTS) chart is assessed using total and generalized variances. By comparing the effectiveness of the L‐Comoments‐based TS chart using simulated and renewable energy data, the new chart based on the proposed approach outperforms the traditional chart and robust charts based on powerful estimators such as the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD). Hence, the new approach enables the new exploration of robust and reliable multivariate quality control analysis for high‐dimension and complex datasets.