Phase I Ridge-Regularised Multivariate Coefficient of Variation Control Charts for High-Dimensional Processes Under Localised Contamination

Abstract

Phase I monitoring of the multivariate coefficient of variation (MCV) is essential for establishing stable control limits. Yet, it remains underexplored in high-dimensional settings, where classical covariance matrix estimators often become singular, and variables are correlated. This study addresses this gap by proposing a Phase I monitoring framework that uses an alternative ridge estimator (Altridge) within a penalised likelihood framework. The estimation procedure adapts the Reyment, Voinov-Nikulin, and Albert-Zhang MCV formulations to yield stable, positive-definite covariance estimates, specifically targeting scenarios with localised contamination and high- dimensionality (p≥n); using probability to  signal (PTS) as a performance metric. Significant findings from extensive Monte Carlo simulations demonstrate that the proposed Altridge charts provide stable estimation and effectively detect process disturbances, with detection probability increasing alongside shift magnitudes (δ) and contamination
levels (m^1 ). Notably, the Albert-Zhang-based chart consistently exhibits the highest sensitivity among the three methods due to a computational structure that avoids direct matrix inversion, making it more robust against numerical instability. A real-life application to a breast cancer diagnostic dataset confirms the practical implication of this framework; it successfully identifies abnormal variability patterns within a complex, correlated biomedical dataset, establishing the methodology as a reliable toolfor high-dimensional Phase I process monitoring.