A Distribution-Free Multivariate Control Chart for Phase I Applications

Abstract

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 T-2 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. Copyright (c) 2014 John Wiley & Sons, Ltd.