Statistical Process Control for Variance Shift Detections of Multivariate Autocorrelated Processes

Abstract

A statistical process control (SPC) approach is proposed to detect variance changes in a multivariate autocorrelated process. The initial step involves a multivariate dynamic linear model (DLM) to remove the autocorrelated data structure. Then diagonal elements of the variance-covariance matrix are then calculated from sample residual vectors obtained from DLM filtering. A multivariate exponential weighted moving average (EWMA) control chart is applied to the vectors of diagonal elements. The proposed control charts called MEWMV for monitoring multivariate variance responses are compared to a multivariate sample generalized variance | S | charts, individual S charts and individual EWMS control charts in term of average run length (ARL). Simulation results based on bivariate AR(1) data show that the proposed MEWMV chart applying to observations without log transformation performs the best for various magnitudes of variance shifts regardless of sample sizes and autocorrelation structures.