A Distribution-Free Multivariate Control Chart for Phase I Applications

The purpose of this paper is to provide a novel distribution‐free control chart for monitoring the location parameter vector of a multivariate process in phase I analysis. To be robust to the process distribution, the spatial sign statistic that defines the multivariate direction of an observation is used to construct a Shewhart‐type control chart for detecting out‐of‐control observations in historical phase I data. The proposed control chart is distribution free in the sense that the false‐positive rate (or false alarm rate), the proportion of wrongly classified in‐control samples, can be controlled at the specified value for elliptical‐direction distributions. In addition, we demonstrate through simulation studies that the false‐positive rate of the proposed chart is robust to the shift size of the out‐of‐control condition if we only delete the most extreme out‐of‐control observation at each iteration of phase I analysis. Compared with the traditional Hotelling's T² control chart and some of its robust versions, the proposed chart is generally more powerful in detecting out‐of‐control observations and more robust to the normality assumption.