Study and improvement of a multivariate covariance control chart based on the Sparse Group Lasso penalty

Traditional multivariate parametric control charts often perform inadequately in detecting shifts in the covariance matrix when the data deviate from normality. In this paper, we propose a multivariate nonparametric exponentially weighted moving average (SGLGEWMA) control chart, incorporating a Sparse Group Lasso penalty, which is capable of detecting shifts in the covariance matrix across a wide range of data types, including discrete, continuous, and mixed distributions. The proposed approach projects multivariate data into a Euclidean space and then computes an approximate Alt's likelihood ratio, regularized via the Sparse Group Lasso. The resulting EWMA statistic monitors process shifts. Monte Carlo simulations demonstrate that SGLGEWMA outperforms both the Lasso-based LGShewhart and the Ridge-based RGEWMA control charts under various distributions, with enhanced efficacy in high-dimensional scenarios. Sensitivity analyses are performed on the tuning parameters ([Formula: see text], [Formula: see text]) and smoothing parameter ρ, to evaluate their impact on monitoring performance. Additionally, a simulation study and an illustrative example involving covariance monitoring in wafer semiconductor manufacturing are presented to demonstrate the practical application of the proposed chart. Empirical results confirm that the proposed control chart promptly identifies abnormal fluctuations and issues timely alerts, highlighting both its theoretical significance and practical utility.