Monitoring high-dimensional heteroscedastic processes using rank-based EWMA methods

Monitoring high-dimensional processes is a challenging task, as the underlying dependency structure among variables is often too complicated to estimate accurately. The inherent volatility of dependence, so-called heteroscedasticity, is rarely mentioned nor considered in process monitoring problems. We consider time-dependent heteroscedasticity a common cause variability and propose an integrated scheme for monitoring and diagnosis of changes in the location parameters of high-dimensional processes. Our proposed method consists of rank-based EWMA control charts which are designed to detect mean shifts in a small subset of variables. A bootstrap algorithm determines the control limits by achieving a pre-specified false alarm probability. A post-signal diagnosis strategy is executed to cluster the shifted variables and estimate a time window for the change point. Simulation results show that the proposed methodology is robust to heteroscedasticity and sensitive to small and moderate sparse mean shifts. It can efficiently identify out-of-control variables and the corresponding change points. A real-life example of monitoring online vibration data for predictive maintenance applications illustrates the proposed methodology.