The GLRT for statistical process control of autocorrelated processes

Abstract

This paper presents an on-line Statistical Process Control (SPC) technique, based on a Generalized Likelihood Ratio Test (GLRT), for detecting and estimating mean shifts in autocorrelated processes that follow a normally distributed Autoregressive Integrated Moving Average (ARIMA) model. The GLRT is applied to the uncorrelated residuals of the appropriate time-series model. The performance of the GLRT is compared to two other commonly applied residual-based tests - a Shewhart individuals chart and a CUSUM test. A wide range of ARIMA models are considered, with the conclusion that the best residual-based test to use depends on the particular ARIMA model used to describe the autocorrelation. For many models, the GLRT performance is far superior to either a CUSUM or Shewhart test, while for others the difference is negligible or the CUSUM test performs slightly better. Simple, intuitive guidelines are provided for determining which residual-based test to use. Additional advantages of the GLRT are that it directly provides estimates of the magnitude and time of occurrence of the mean shift, and can be used to distinguish different types of faults, e.g., a sustained mean shift versus a temporary spike.

Additional information

Notes on contributors

DANIEL W. APLEY

Daniel W. Apley received B.S. and M.S. degrees in Mechanical Engineering, an M.S. degree in Electrical Engineering, and a Ph.D. degree in Mechanical Engineering in 1990, 1992, 1995, and 1997, respectively, all from the University of Michigan. He was a visiting researcher at the Institute for Machine Tools and Factory Management, Technical University of Berlin, in 1995. Since 1998, he has been with the Texas A&M University, where he is currently an Assistant Professor of Industrial Engineering. Dr. Apley's research area is quality assurance in manufacturing processes through in-process sensing and model-based statistical process monitoring, diagnosis, and adaptive feedback compensation. His recent research has been applied to chatter monitoring and suppression in machining, multivariate statistical process control and root cause diagnosis in autobody assembly, and active balancing of rotating machinery. He received an AT&T Bell Laboratories Ph.D. Scholarship from 1993 to 1997 and is a member of IIE, JEEE, ASME, and SME.

JIANJUN SHI

Jianjun (Jan) Shi is an Assistant Professor in the Department of Industrial and Operations Engineering a t the University of Michigan. He received his B.S. and M.S. degrees in Electrical Engineering at the Beijing Institute of Technology in 1984 and 1987 respectively, and received his Ph.D. in Mechanical Engineering at the University of Michigan in 1992. Professor Shi's research interests are the fusion of advanced statistics and engineering knowledge to develop In-Process Quality Improvement (IPQI) methodologies achieving automatic process monitoring, diagnosis, compensation, and their implementation in various manufacturing processes. He has supervised six Ph.D. graduates and published more than 40 papers in this area. He received the NSF CAREER award in 1996, the Departmental Excellent Research Award at the University of Michigan in 1997, and the 1938E Award of the Collage of Engineering at the University of Michigan in 1998. His current research activities are sponsored by the General Motors Corporation, the Chrysler Corporation, Auto Body Consortium, National Institute of Standards and Technology - Advanced Technology Program, and the National Science Foundation. He serves as the director of the IPQI Research Lab in the IOE Department, the Associate Director of the S. M. Wu Manufacturing Research Center, and Program Technical Director a t Auto Body Consortium. He is currently serving on the Editorial Board of IIE Transacrions on Quality and Reliability. He is a member of ASME, ASQC, IIE, and SME.