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

• Proposed a multivariate EWMA chart for finite horizon production (FHP) process. • The proposed method is based on the rank-energy statistic. • Demonstrated efficiency by validating results against parametric benchmarks. • Account for early and delayed shift in multivariate process. • Real-life case studies included about detection of faults in sensorless drives and steel plates. 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 ( R E 2 ) statistic. The R E 2 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- R E 2 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- R E 2 chart over it's competitors, especially for multivariate processes with skewed distributions.