Nonparametric multivariate CUSUM control charts for location and scale changes

Abstract

Among different multivariate control charts, multivariate cumulative sum (CUSUM) control charts are the popular choice for detecting small and moderate changes in the manufacturing process. However, most of CUSUM procedures in the literature were developed under the multivariate normality assumption. This assumption is usually difficult to justify in practice. In this paper, we propose two new nonparametric multivariate CUSUM procedures based on the spatial sign and data depth for detecting location and scale changes. These two procedures can be considered as the nonparametric counterparts of the two parametric multivariate CUSUM procedures developed in Crosier [(1988), ‘Multivariate Generalizations for Cumulative Sum Quality-Control Schemes’, Technometrics, 30, 291–303]. We show that the two proposed CUSUM procedures are affine invariant and asymptotically distribution-free over a broad family of distributions. In our simulation studies, the proposed CUSUM procedures perform well across a broad range of settings and compare favourably with existing CUSUM procedures for detecting location and scale changes.

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