Spatial rank-based high-dimensional monitoring through random projection

Abstract

High-dimensional process monitoring becomes increasingly important in many applications where the joint distribution of process variables is usually unknown and not normal, and requires nonparametric methods for analysis and monitoring. However, when the process dimension is much larger than the reference sample size, most traditional nonparametric multivariate control charts fail due to the curse of dimensionality. Furthermore, when the process goes out of control, only a few (sparse) dimensions will be influenced, which increases the difficulty for both detection and diagnosis. To address these problems, this article proposes a new nonparametric monitoring scheme for high-dimensional processes. This scheme first projects the high-dimensional process into several subprocesses using ensemble random projections for dimension reduction. Then, for each subprocess a local nonparametric control chart is constructed based on the spatial rank test. Finally, all the local charts are fused together for decision making. Furthermore, after an out-of-control alarm is triggered, a diagnostic framework is proposed based on the square-root LASSO algorithm. Numerical studies together with real-data examples demonstrate the efficacy and applicability of the proposed methodology.

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