Multivariate control chart with a deployed matrix for autocorrelated data

Abstract

Abstract Over the last years, multivariate statistical process control (MSPC) methods and namely principal component analysis (PCA) have shown to provide a powerful approach to detection and isolation of abnormal conditions in process industries with highly correlated variables. This paper presents a new control chart that follows the same philosophy as DPCA chart but introduces a new matrix structure with deployed columns that allows canceling autocorrelation in the score variables. A comparative performance study between the well-known Hotelling's T 2 control chart (using residuals or one-step-ahead predictions), the dynamic PCA (DPCA) chart and the new proposed control chart named as DMPCA (Deployed Matrix PCA) is presented. The approach developed to compare those charts is described in detail, using the average run length (ARL) and correspondent SDRL (standard deviation run length) as a performance indicator. Monte Carlo experiments are used to simulate three variables following different autocorrelated structures (AR and ARMA) and without cross correlation between them. The main advantages and disadvantages of each chart are pointed out, in the practical perspective of those who intent to use MSPC to monitor dynamic continuous processes with a small number of variables to be controlled. This study reveals considerable improvements regarding the use of DMPCA to detect small to moderate shifts in the mean process parameter when compared with DCPA and huge improvements when compared with T 2 Hotelling's Chart.