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.

Key Words:

• Autoregressive
• control chart
• dynamic linear model
• EWMA
• multivariate time series
• SPC

Additional information

Notes on contributors

Shing I. Chang

Shing I Chang Associate Professor in the Department of Industrial and Manufacturing Systems Engineering at Kansas State University. His research interests include multivariate control charts, change point analysis, nonlinear profile monitoring, optimal experimental designs, and soft computing techniques applied to quality engineering and health care related problems. He served the president of the Quality Control and Reliability Engineering Division of Institute of Industrial Engineers in 1996–1997. He currently serves as a Department Editor of the Process Monitoring and Control area in the Quality and Reliability Engineering Focus Issue of IIE Transactions. Dr. Chang is a senior member of both Institute of Industrial Engineers and American Society for Quality.

Kui Zhang

Kui Zhang Received his M.S. degree from the Department of Industrial and Manufacturing Systems Engineering at Kansas State University in 2000. This paper is based on his master’s thesis for his IMSE MS degree.