Multivariate nonparametric control charts based on projection pursuit

Multivariate nonparametric control charts are highly sought-after due to their flexibility to adapt to different distribution assumptions. However, many of the existing multivariate nonparametric control charts are only distribution-free for certain distribution families. Although those distribution families may contain different distributions, it is still difficult to verify whether the underlying multivariate distribution from a particular application belongs to those distribution families in practice. A few existing multivariate nonparametric control charts are fully nonparametric. As shown in the literature and in our simulation studies, most of them are not efficient in detecting location shifts. In this paper, we propose a new multivariate nonparametric control chart based on the idea of projection pursuit. The proposed control chart is fully nonparametric and can be applied to any multivariate distribution as long as its covariance matrix exists. The control limit of the proposed control chart only depends on the nominal ARL0$\text{ARL}_0$, which makes its implementation much easier. Our simulation study and real data analysis show that the proposed control chart performs well across a variety of settings, and compares favorably with existing multivariate nonparametric control charts.