On Nonparametric Statistical Process Control of Univariate Processes

This paper considers statistical process control (SPC) of univariate processes when the parametric form of the process distribution is unavailable. Most existing SPC procedures are based on the assumption that a parametric form (e.g., normal) of the process distribution can be specified beforehand. In the literature, it has been demonstrated that their performance is unreliable in cases when the pre-specified process distribution is invalid. To overcome this limitation, some nonparametric (or distribution-free) SPC control charts have been proposed, most of which are based on the ordering information of the observed data. This paper tries to make two contributions to the nonparametric SPC literature. First, we propose an alternative framework for constructing nonparametric control charts, by first categorizing observed data and then applying categorical data analysis methods to SPC. Under this framework, some new nonparametric control charts are proposed. Second, we compare our proposed control charts with several representative existing control charts in various cases. Some empirical guidelines are provided for users to choose a proper nonparametric control chart for a specific application. This article has supplementary materials online.