Control Charts for Multivariate Processes

Abstract This article uses the concept of data depth to introduce several new control charts for monitoring processes of multivariate quality measurements. For any dimension of the measurements, these charts are in the form of two-dimensional graphs that can be visualized and interpreted just as easily as the well-known univariate X, X, and CUSUM charts. Moreover, they have several significant advantages. First, they can detect simultaneously the location shift and scale increase of the process, unlike the existing methods, which can detect only the location shift. Second, their construction is completely nonparametric; in particular, it does not require the assumption of normality for the quality distribution, which is needed in standard approaches such as the χ2 and Hotelling's T 2 charts. Thus these new charts generalize the principle of control charts to multivariate settings and apply to a much broader class of quality distributions.