Design variable-sampling control charts using covariate information

Abstract

Statistical Process Control (SPC) charts are widely used in manufacturing industry for monitoring the performance of sequential production processes over time. A common practice in using a control chart is to first collect samples and take measurements of certain quality variables from them at equally-spaced sampling times, and then make decisions about the process status by the chart based on the observed data. In some applications, however, the quality variables are associated with certain covariates, and it should improve the performance of an SPC chart if the covariate information can be used properly. Intuitively, if the covariate information indicates that the process under monitoring is likely to have a distributional shift soon based on the established relationship between the quality variables and the covariates, then it should benefit the process monitoring by collecting the next process observation sooner than usual. Motivated by this idea, we propose a general framework to design a variable-sampling control chart by using covariate information. Our proposed chart is self-starting and can well accommodate stationary short-range serial data correlation. It should be the first variable-sampling control chart in the literature that the sampling intervals are determined by the covariate information. Numerical studies show that the proposed method performs well in different cases considered.

Keywords:

• Auxiliary variables
• data correlation
• kernel estimation
• regression modelling
• sampling intervals
• self-starting
• statistical process control
• variable-sampling

Acknowledgments

The authors thank the editors and three referees for their constructive comments and suggestions, which improved the quality of the paper greatly.

Additional information

Funding

This research is supported in part by the NSF grant DMS-1914639.

Notes on contributors

Kai Yang

Kai Yang is currently a PhD student in the Department of Biostatistics at the University of Florida. His thesis research mainly concerns spatio-temporal data modeling and monitoring and is supervised by Professor Peihua Qiu. He has published five papers on nonparametric estimation of the mean and variance/covariance structures of spatial data, and on spatio-temporal data monitoring. In addition to that topic, his thesis research also discusses effective process monitoring by using covariate information.

Peihua Qiu

Peihua Qiu received his PhD in statistics from the Department of Statistics at the University of Wisconsin - Madison in 1996. He worked as a senior research consulting statistician of the Biostatistics Center at the Ohio State University during 1996–1998. 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 of 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 has served as an associate editor for Journal of the American Statistical Association, Biometrics, Technometrics, Surgery, and Statistical Papers, 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 an associate editor of Quality Engineering, and a Professor and the Founding Chair of the Department of Biostatistics at the University of Florida.

Peihua Qiu 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 130 research papers in referred journals, many of which have appeared in top 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 IISE 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.