The advent of larger manufacturing databases has greatly increased the use of multivariate quality control methods in recent years. Another important application area for multivariate control charts is in the monitoring of profiles, where a quality characteristic can be expressed as a modeled function of one or more explanatory variables. There are two distinct phases in the implementation of control charts. Phase I involves the analysis of a dataset to establish the in-control (IC) state of the process and identify a baseline reference sample and then the IC reference sample can be used to establish control limits for Phase II that is the monitoring stage of a control charting application. In Phase II, process observations are prospectively compared with the control limits to identify significant departures from the IC state. The purpose of this article is to introduce a Phase I method to detect either isolated or sustained shifts in the location vector of a multivariate process. The control chart method introduced is based on the concept of ranking data. Because ranking observations in multivariate space may be unfamiliar, an area of computational geometry known as data depth is introduced. A Monte Carlo simulation study comparing the performance of our proposed method with the Phase I hotelling's T~2 chart is provided. An example application of the proposed method and advice to practitioners for moving from a Phase I to a Phase II analysis id also provided (48 refs.)
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