Anomaly detection of multivariate finite-horizon process based on the rank-energy statistic

In this Industry 5.0 era, many online production processes resemble multivariate Finite Horizon Production (FHP) process, a time-bound stochastic process characterized by several variables. While the literature on monitoring multivariate FHP processes is scarce, these methods often rely heavily on the assumption of a multivariate normal distribution, which is challenging to achieve in real-world applications. To address this limitation, this article proposes a non-parametric exponentially weighted moving average (EWMA) control chart based on the rank-energy (RE²) statistic. The RE² test, founded on the measure transportation theory, offers a robust approach for detecting shifts in multivariate process distributions. The robustness and anomaly detection ability of the proposed EWMA-RE² chart is assessed using Monte Carlo simulations. Two real-world industrial production datasets are used to demonstrate the practical relevance for industrial applications. The proposed method displayed a stable performance for a reference sample of size more than 50 (m>50). Comparison study demonstrates a superior robustness and efficient shift detection ability of the proposed EWMA-RE² chart over it's competitors, especially for multivariate processes with skewed distributions.