Statistical Process Control Using a Dynamic Sampling Scheme

Abstract

This article considers statistical process control (SPC) of univariate processes, and tries to make two contributions to the univariate SPC problem. First, we propose a continuously variable sampling scheme, based on a quantitative measure of the likelihood of a process distributional shift at each observation time point, provided by the p-value of the conventional cumulative sum (CUSUM) charting statistic. For convenience of the design and implementation, the variable sampling scheme is described by a parametric function in the flexible Box–Cox transformation family. Second, the resulting CUSUM chart using the variable sampling scheme is combined with an adaptive estimation procedure for determining its reference value, to effectively protect against a range of unknown shifts. Numerical studies show that it performs well in various cases. A real data example from a chemical process illustrates the application and implementation of our proposed method. This article has supplementary materials online.

• Adaptive estimation
• Bootstrap
• Monte Carlo simulation
• Variable sampling

ACKNOWLEDGMENTS

The authors are grateful to the editor, the associate editor, and two anonymous referees for their valuable comments that have greatly improved the article. Part of this research is finished during Li’s visit to School of Statistics at The University of Minnesota, whose hospitality is appreciated. The research is supported in part by an NSF grant, by the Natural Sciences Foundation of China grants 11201246, 11071128, and 11131002, the RFDP of China Grant 20110031110002, and the Office of International Programs at The University of Minnesota.