Generalized smoothing parameters of a multivariate EWMA control chart

ABSTRACT

The Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is effective in detecting a small process mean shift. Its simplicity and generality stem from the assumption that the smoothing parameters of the variables are given constants and equally distributed on the diagonal of the smoothing matrix. Recently, the MEWMA model with the full non-diagonal smoothing matrix (FEWMA) is studied. The model, however, has limited use due to the assumption that the off-diagonal elements are the same; therefore, it would necessarily be sensitive to the correlation structure of observations. In this article, we propose a generalized model for the MEWMA, that uses appropriate non-diagonal elements in the smoothing matrix based on the correlation among variables. We also offer an interpretation of off-diagonal elements of the smoothing matrix and suggest an optimal design for a proposed MEWMA chart. A case study on the automatic monitoring of dimensions of bolts using an imaging processing system is presented to illustrate the proposed control chart. The proposed model is effective in detecting small mean shifts and shows improved performance when compared with MEWMA, FEWMA, and other recently improved control charts.

KEYWORDS:

• Average run length
• multivariate exponentially weighted moving average
• optimal design
• smoothing matrix

Acknowledgement

The authors thank the anonymous reviewers and editors for their helpful and constructive comments that greatly contributed to improving this paper.

Funding

Part of this work was supported by the National Science Foundation of the USA (grant no. 1233800).

Additional information

Notes on contributors

Sangahn Kim

Sangahn Kim received his B.S. degree in Business Administration from Ajou University, Korea, in 2004 and M.S. degree in Industrial and Systems Engineering from Sungkyunkwan University, Korea, in 2006. He is currently a Ph.D. candidate in the Department of Industrial and Systems Engineering, Rutgers University. He is a recipient of the Richard A. Freund International Scholarship in 2016. His research interests include statistical process modeling and monitoring, reliability engineering, data mining, and stochastic processes.

Myong K. Jeong

Myong K. Jeong is an Associate Professor in the Department of Industrial and Systems Engineering at Rutgers University. He was formerly an Assistant Professor in the Department of Industrial and Information Engineering, the University of Tennessee, Knoxville. He worked as a senior researcher from 1993 to 1999 at the Electronics and Telecommunications Research Institute (ETRI). He has focused on developing data mining techniques, process monitoring and control procedures, and optimization techniques for machine learning. His research has been supported by the National Science Foundation, National Transportation Research Center, United States Department of Agriculture, Qatar National Research Fund, Electronics and Telecommunications Research Institute, and various industries. He has been a consultant for Samsung Electronics, ETRI, KISTI, and other companies. He is an Associate Editor of IEEE Transactions on Automation Science and Engineering and International Journal of Quality, Statistics and Reliability and an Advisory Board Member of the International Journal of Advanced Manufacturing Technology. He is a senior member of IEEE.

Elsayed A. Elsayed

Elsayed A. Elsayed is a Distinguished Professor in the Department of Industrial and Systems Engineering at Rutgers University, New Jersey. His research interests are in the areas of quality and reliability engineering and production planning and control. He is the author of Reliability Engineering (John Wiley & Sons, 2012). He is the author and co-author of work published in IIE Transactions and the International Journal of Production Research. His research has been funded by the DoD, FAA, NSF, and industry. He has been a consultant for the DoD, AT&T Bell Laboratories, Ingersoll-Rand, Johnson & Johnson, Personal Products, AT&T Communications, Ethicon, and other companies. He was the Editor-in-Chief of IIE Transactions and the Editor of IIE Transactions on Quality and Reliability Engineering. He is also an Editor for the International Journal of Reliability, Quality and Safety Engineering.