Robust Monitoring of Multivariate Location Using a New Nonparametric Depth-Based Control Chart

Monitoring multivariate processes under nonnormal conditions remains a persistent challenge in statistical process control, as most classical control charts rely heavily on distributional assumptions. To address this limitation, this paper proposes a depth-based Shewhart-type control chart, denoted by LD2, which detects shifts in multivariate location through discrepancies in data-depth profiles. The proposed framework is implemented using three widely studied depth functions—Mahalanobis, halfspace, and simplicial depth—and its performance is evaluated in comparison with Hotelling's T2 and Randles' Rn charts. Extensive Monte Carlo simulations under normal, heavy-tailed, and light-tailed distributions indicate that the LD2 chart maintains stable in-control performance while providing improved sensitivity to small and moderate shifts, particularly in the presence of skewness or heavy tails. Among the depth functions considered, the simplicial-depth-based version consistently demonstrates superior detection capability in non-Gaussian settings. The practical effectiveness of the proposed method is illustrated through a real-data application to wine-quality monitoring, where the LD2 chart identifies a larger proportion of out-of-control subgroups compared with classical approaches. These results suggest that LD2 provides a flexible and robust alternative for multivariate process monitoring when standard normality assumptions are violated.