Residual-based maximum MCUSUM control chart for joint monitoring the mean and variability of multivariate autocorrelated processes

Maximum multivariate cumulative sum (Max-MCUSUM) is one of the single control charts proposed for joint monitoring the mean and variability of independent observation. Since many applications yield time series data, it is important to develop Max-MCUSUM control chart for monitoring multivariate autocorrelated processes. In this paper, we propose a Max-MCUSUM control chart based on the residual of multioutput least square support vector regression (MLS-SVR). The optimal parameters of MLS-SVR model are calculated using historical in-control data and the control limit of the proposed chart is estimated using the bootstrap approach. The average run lengths of MLS-SVR-based Max-MCUSUM chart verify that the proposed chart is more sensitive to detect mean vector shift than to detect a covariance matrix shift. The illustrative examples of the proposed control chart are also provided for both simulation and real data.