Nonparametric multivariate CUSUM control charts for location and scale changes. (English) Zbl 1297.62251
Summary: 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 [R. B. Crosier, Technometrics 30, No. 3, 291–303 (1988; Zbl 0651.62095)]. 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.
MSC:
| 62P30 | Applications of statistics in engineering and industry; control charts |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G30 | Order statistics; empirical distribution functions |
| 62H11 | Directional data; spatial statistics |
Citations:
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