A machine learning-based statistical process control for nonnormal multivariate data with nonlinear correlation structure

Arijit Maji

doi:10.1080/01605682.2026.2679041

A machine learning-based statistical process control for nonnormal multivariate data with nonlinear correlation structure

2026-06-12

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DOI：10.1080/01605682.2026.2679041

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Multivariate process control (MPC) charts are widely used to simultaneously monitor multiple quality characteristics to ensure manufacturing quality, productivity, and operational stability. However, most existing distribution-free MPC charts focus mainly on monitoring ‘location’ or ‘dispersion’ parameters, often assume linear or negligible correlation structures, and provide limited capability for diagnosing the sources of out-of-control (OC) signals. To address these limitations, this paper proposes a real-time distribution-free framework for joint monitoring and diagnosis of multivariate processes with nonlinear dependence. The proposed control chart simultaneously monitors ‘location’, ‘dispersion’, and ‘asymmetry’ through a single statistic for individual independent observations. The framework integrates a robust ‘spatial median’ estimator, k-nearest neighbour (k-NN)-based local dispersion estimation with optimally selected neighbourhood size, and one-class classifier support vector machine (OCC-SVM), referred to as the ‘Spatial-median and k-NN-based OCC-SVM’ chart. A new unsupervised bi-objective optimisation approach is introduced for hyperparameter tuning of OCC-SVM. For diagnosis, a ‘relative-indicator’-based decomposition identifies variable-level contributions to an OC signal, with support vectors used to determine diagnostic thresholds. Monitoring performance is evaluated through extensive Monte–Carlo simulations under three nonlinear correlation structures, considering both abrupt and gradual shifts, using the median run length (MRL) and the Relative Median Index (RMeI). For the diagnosis performance, a subset of process variable shifts is considered. Results show consistently superior monitoring (lower OC-MRL and RMeI) and diagnostic accuracy compared to competing methods, and its practical effectiveness is further validated through three real manufacturing case studies.

Keywords:

Distribution-free control charts

Multivariate process control

Machine learning–based SPC

Nonlinear dependence

Online monitoring

Process diagnosis

A machine learning-based statistical process control for nonnormal multivariate data with nonlinear correlation structure

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