A Directional Multivariate Sign EWMA Control Chart

Abstract

AbstractIn many applications the shift directions of observation vectors are limited, which allows focusing detection power on a limited subspace with improved sensitivity. This paper develops a new multivariate nonparametric statistical process control chart for monitoring location parameters, which is based on integrating a directional multivariate spatial-sign test and exponentially weighted moving average control scheme to on-line sequential monitoring. The computation speed of the proposed scheme is fast with a similar computation effort to its parametric counterpart, regression-adjusted control charts. It has a distribution-free property over a broad class of population models, which implies the in-control run length distribution can attain or is always very close to the nominal one when using the same control limit designed for a multivariate normal distribution. This proposed control chart possesses some other appealing features. Simulation studies show that it is efficient in detecting small or moderate shifts, when the process distribution is heavy-tailed or skewed. Finally, a specific SPC example, multistage process control, is also presented to demonstrate the effectiveness of our method.Key Words: Distribution-freemultivariate regression-adjusted chartnonparametric procedurerobustnessspatial sign teststatistical process control. Additional informationNotes on contributorsXuemin ZiXuemin Zi Associate Professor of the School of Science at Tianjin University of Technology and Education. Her research interests include statistical process control and design of experiments.Changliang ZouChangliang Zou Associate Professor of School of Mathematical Sciences, Nankai University. He obtained his B.S, M.S, and Ph.D. in Statistics, from Nankai University, in 2003, 2006, and 2008, respectively. His primary research interests include statistical process control, nonparametric regression and dimension reduction, high-dimensional data analysis. His research has been published in various referred journals in Statistics and Industrial Engineering including Journal of the American Statistical Association, Annals of Statistics, Technometrics, Journal of Quality Technology, IIE Transactions, Statistica Sinica, Naval Research Logistic, Annals of Operation Research, etc.Qin ZhouQin Zhou Assistant Professor of School of Mathematical Sciences, Jiangsu Normal University. Her research interests include statistical process control and health-care system.Jingshen WangJingshen Wang Undergraduate student of School of Mathematical Sciences, Nankai University. Changliang Zou is her final-year project supervisor. Her research interests include statistical process control, semiparametric regression and lack-of-fit test.