Vector Autoregressive-Based Maximum MCUSUM Control Chart for Monitoring the Quality of White Crystal Sugar

Abstract

The white crystal sugar which is widely consumed sugar has two critical to qualities, namely the index of solution colour and the level of sulphur dioxide. These quality characteristics have small mean and variability shifts, as well as autocorrelation pattern. This research aims to propose residual-based Maximum Multivariate Cumulative Sum (Max-MCUSUM) control chart, one of the single control charts to monitor small shifts of mean and variability simultaneously, for monitoring the quality of white crystal sugar. The vector autoregressive (VAR) model is utilized to model the daily solution colour index and the daily sulphur dioxide level, then the residuals are monitored using Max-MCUSUM chart. The VAR-based Max-MCUSUM chart employs bootstrap, one of the nonparametric resampling methods, to estimate the control limit. The results of white crystal sugar quality control show that the processes in the last week of August 2020 need to be improved. Monitoring the white crystal sugar data using conventional control chart leads to many false alarm signals. Furthermore, the proposed control chart is more sensitive than the residual-based MEWMA and residual-based Hotelling’s T 2 charts in case of monitoring the quality of white crystal sugar.