Multivariate CUSUM Chart to Monitor Correlated Multivariate Time-series Observations

Purpose: The purpose of this study is to propose a multivariate CUSUM control chart that can detect the out-of-control state fast while monitoring the cross- and auto- correlated multivariate time series data.Methods: We first build models to estimate the observation data and calculate the corresponding residuals. After then, a multivariate CUSUM chart is applied to monitor the residuals instead of the original raw observation data. Vector Autoregression and Artificial Neural Net are selected for the modelling, and Separated-MCUSUM chart is selected for the monitoring. The suggested methods are tested under a number of experimental settings and the performances are compared with those of other existing methods.Results: We find that Artificial Neural Net is more appropriate than Vector Autoregression for the modelling and show the combination of Separated-MCUSUM with Artificial Neural Net outperforms the other alternatives considered in this paper.Conclusion: The suggested chart has many advantages. It can monitor the complicated multivariate data with cross- and auto- correlation, and detects the out-of-control state fast. Unlike other CUSUM charts finding their control limits by trial and error simulation, the suggested chart saves lots of time and effort by approximating its control limit mathematically. We expect that the suggested chart performs not only effectively but also efficiently for monitoring the process with complicated correlations and frequently-changed parameters.