A nonparametric CUSUM chart for monitoring multivariate serially correlated processes

Abstract

In applications, most processes for quality control and management are multivariate. Thus, multivariate statistical process control (MSPC) is an important research problem and has been discussed extensively in the literature. Early MSPC research is based on the assumptions that process observations at different time points are independent and they have a parametric distribution (e.g., Gaussian) when the process is in-control (IC). Recent MSPC research has lifted the “parametric distribution” assumption, and some nonparametric MSPC charts have been developed. These nonparametric MSPC charts, however, often requires the “independent process observations” assumption, which is rarely valid in practice because serial data correlation is common in a time series data. In the literature, it has been well demonstrated that a control chart who ignores serial data correlation would be unreliable to use when such data correlation exists. So far, we have not found any existing nonparametric MSPC charts that can accommodate serial data correlation properly. In this paper, we suggest a flexible nonparametric MSPC chart which can accommodate stationary serial data correlation properly. Numerical studies show that it performs well in different cases.

Keywords:

• data correlation
• decorrelation
• moment estimation
• nonparametric charts
• stationary data correlation
• statistical process control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We would like to thank the editor and a referee for some constructive comments and suggestions, which improved the quality of the paper greatly. Peihua Qiu’s research was supported in part by the NSF grant DMS-1914639 in USA. Li Xue’s research was supported in part by the grants 71701188, 71672209 and 71871204 from the National Natural Science Foundation of China, the grant 2016M601266 from the China Postdoctoral Science Foundation, the grant 19HASTIT032 from the Science and Technology Innovation Talent Support plan in Universities of Henan Province of China, and the grant 2016GGJS-112 from the Training Program for Young Key Teachers in Universities of Henan Province.

Notes on contributors

Li Xue

Li Xue is Associate Professor and Associate Dean of the College of Information and Management at the Zhengzhou University of Aeronautics. Her major research areas include quality control and management, and big data analytics. She has published over 20 papers in these areas, and her research has been well supported by grants from the National Science Foundation of China, Aeronautic Science Foundation of China, and other grant agencies. This paper was mainly based on her joint research with Professor Peihua Qiu during the recent one-year visit at the University of Florida in the USA.

Peihua Qiu

Peihua Qiu is Professor and Founding Chair of the Department of Biostatistics at the University of Florida. He is an elected fellow of the American Statistical Association, an elected fellow of the Institute of Mathematical Statistics, and an elected member of the International Statistical Institute. He was the editor of Technometrics and served as associate editor for a number of top journals, including the Journal of the American Statistical Association, Biometrics, and Technometrics. He has made substantial contributions in several research areas, including jump regression analysis, image processing, statistical process control, survival analysis, and disease screening and surveillance. So far, he has published over 125 research papers, many of which appeared in top journals.