ABSTRACT Complex processes involving multiple linearly correlated variables typically possess a low intrinsic dimension, so the observed high‐dimensional data are considered to be determined by low‐dimensional latent vectors. Principal component analysis (PCA) is commonly used to identify this latent structure and thereby construct monitoring statistics. However, the assumption of normality makes PCA difficult to handle heavy‐tailed data. To this end, the Probabilistic PCA (PPCA) for ‐distributions is employed to model heavy‐tailed data with a latent structure, namely ‐PPCA. Employing the ‐PPCA model, we further exploit shift directions to narrow down possible shifts to one of several mutually orthogonal directions, which can enhance detection power and facilitate diagnosis. The proposed directional monitoring statistic includes many commonly used monitoring statistics as special cases when appropriate shift directions are selected, such as those in the principal component and residual subspaces as well as that for detecting single‐variable shifts. Numerical simulations and a case study have demonstrated the power of the proposed methods.
X et al. (Mon,) studied this question.