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ABSTRACT
Profile monitoring is used to check the stability of the functional relationship of the process response on several predictors. In most of the existing literature, the monitored functional relationship usually involves only one covariate and the coefficient of the covariate is assumed to be constant. In some applications, the process response depends on multiple covariates, and the functional relationship is not constant but dynamic over time, which is different from those studied in the literature. To implement profile monitoring in these applications, a semiparametric random time-varying coefficient model is employed to characterize this dynamic relationship over time. Based on this model, a profile monitoring scheme integrated with dynamic probability control limits is proposed, which can adapt to the case of the within-profile autocorrelation and arbitrary design points. In Phase I, this paper uses a backfitting iterative procedure with the REML-Based EM-Algorithm to estimate the model. In Phase II, an exponentially weighted moving average scheme on residuals with dynamic probability control limits is developed. The simulation results show that the proposed scheme performs better in many scenarios. Finally, an application to industrial busbar running process monitoring is given to illustrate the scheme’s implementation.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability statement
The data that support the findings of this study are available from the corresponding author, Shuguang He, upon reasonable request.
Additional information
Funding
Notes on contributors
Wei Zhang
Wei Zhang is a D.Eng candidate in the College of Management and Economics at Tianjin University, China. He received his MS degree from Tianjin University of Science and Technology, China, in Mar. 2017. His research interests include statistical process control and quality management.
Zhen He
Zhen He is a professor in College of Management and Economics at Tianjin University, China. He is the head of the Department of Industrial Engineering. He is an academician of the International Academy for Quality (IAQ). His research interests are Lean Six Sigma, quality engineering and quality management, statistical quality control.
Shuguang He
Shuguang He is a professor in College of Management and Economics, Tianjin University, China. He received his PhD degree in management science and engineering from Tianjin University, China, in 2002. His research interests are warranty data analysis, statistical quality control and quality management.
Zhanwen Niu
Zhanwen Niu is a professor in College of Management and Economics, Tianjin University, China. He received his PhD degree in mechanical design & manufacturing and their automation from Tianjin University, China, in 1993. His research interests are industrial engineering theory method and application, enterprise operation management, and manufacturing services and management. He has published more than 40 papers in research journals.
Lisha Song
Lisha Song is an assistant professor in the College of Science at North China University of Technology, China. She earned received her PhD degree in business administration from Tianjin University, China. And she received her MS degree in statistics from Nanjing Normal University, China. Her research interests include statistical process control and profile monitoring.