An efficient and unified statistical monitoring framework for multivariate autocorrelated processes

In current manufacturing and service systems, product quality or process status is typically characterized by multiple variables. The rapid advances of information technologies further make these multiple variables measured at a high-frequent manner and thus generate temporally correlated multivariate data. The statistical monitoring of such a multivariate autocorrelated process (MAP) is quite challenging due to the complicated correlation between different variables and different time lags. To solve this challenge, our paper proposes an efficient and unified MAP monitoring framework. The original serially-dependent multivariate vectors are first represented by a sequence of two-dimensional matrices that contain full information about the mean, cross- correlation and autocorrelation of MAP data. Then a matrix normal distribution with parsimonious properties is adopted to model these constructed matrix data, where a mean parameter is used to characterize the process mean and two covariance matrix parameters are used to capture the cross-correlation and autocorrelation, respectively. Finally, a powerful likelihood ratio test-based charting statistic is analytically derived which can jointly monitor process mean and variability. The superiority of our control chart has been validated by large-scale numerical experiments and areal case study of the Tennessee Eastman benchmark process.