A general charting scheme for monitoring serially correlated data with short-memory dependence and nonparametric distributions

Abstract

Traditional statistical process control charts are based on the assumptions that process observations are independent and identically normally distributed when the related process is In-Control (IC). In recent years, it has been demonstrated in the literature that these traditional control charts are unreliable to use when their model assumptions are violated. Several new research directions have been developed, in which new control charts have been proposed for handling cases when the IC process distribution is nonparametric with a reasonably large IC data, when the IC process distribution is unknown with a small IC data, or when the process observations are serially correlated. However, existing control charts in these research directions can only handle one or two cases listed above, and they cannot handle all cases simultaneously. In most applications, it is typical that the IC process distribution is unknown and hard to be described by a parametric form, the process observations are serially correlated with a short-memory dependence, and only a small to moderate IC dataset is available. This article suggests an effective charting scheme to tackle such a challenging and general process monitoring problem. Numerical studies show that it works well in different cases considered.

Keywords:

• Data correlation
• in-control data
• nonparametric
• online monitoring
• self-starting chart
• statistical process control

Acknowledgments

The authors appreciate the constructive comments and suggestions from the focus issue editor, Professor Judy Jin, and the two referees, which greatly improved the quality of the paper. This research was finished during the one-year visit of the first author at the Department of Biostatistics at the University of Florida.

Additional information

Notes on contributors

Wendong Li

Wendong Li is currently a Ph.D. student at the School of Statistics at the East China Normal University in Shanghai, China. He visited the Department of Biostatistics of the University of Florida as a visiting student between October 2017 and October 2018. His major research areas include statistical process control, quality management, change-point detection, and many different applications.

Peihua Qiu

Peihua Qiu received his Ph.D. in statistics from the Statistics Department at the University of Wisconsin at Madison in 1996. He worked as a senior research consulting statistician of the Biostatistics Center at the Ohio State University between 1996 and 1998. He then worked as an assistant professor (1998-2002), an associate professor (2002-2007), and a full professor (2007-2013) at the School of Statistics at the University of Minnesota. He is an elected fellow of the American Statistical Association, an elected fellow of the Institute of Mathematical Statistics, an elected member of the International Statistical Institute, a senior member of the American Society for Quality, and a lifetime member of the International Chinese Statistical Association. He served as associate editor for Journal of the American Statistical Association (2006-2012), Biometrics (2011-2012), Technometrics (2007-2012), and Statistical Papers (2011-2012), and guest co-editor for Multimedia Tools and Applications, and Quality and Reliability Engineering International. He was the editor-elect (2013) and editor (2014-2016) of Technometrics. He is currently the associate editor of Surgery and Quality Engineering, and the founding chair of the Department of Biostatistics at the University of Florida.

He has made substantial contributions in the areas of jump regression analysis, image processing, statistical process control, survival analysis and disease screening and surveillance. So far, he has published over 100 research papers, many of which appeared in major journals, including Technometrics, Journal of the American Statistical Association, Annals of Statistics, Annals of Applied Statistics, Journal of the Royal Statistical Society (Series B), Biometrika, Biometrics, IEEE Transactions on Pattern Analysis and Machine Intelligence, and IIE Transactions. His research monograph titled Image Processing and Jump Regression Analysis (2005, Wiley) won the inaugural Ziegel prize in 2007 for its contribution in bridging the gap between jump regression analysis in statistics and image processing in computer science. His second book titled Introduction to Statistical Process Control was published in 2014 by Chapman & Hall/CRC.