A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances. (9th October 2018) - Shu, Lianjie; Fan, Jinyu
Abstract : With rapid advances in sensing technology and data acquisition systems, high‐dimensional data appear in many settings. The high dimensionality presents a new challenge to the traditional tools in multivariate statistical process control, due to the "curse of dimensionality." Various tests for mean vectors in high dimensional situations have been discussed recently; however, they have been rarely adapted to process monitoring. This paper develops a distribution‐free control chart based on interpoint distances for monitoring mean vectors in high‐dimensional settings. Other than the Euclidean distance, the family of Minkowski distance is used for discussion, which is a generalization of the former and other distances. The proposed approach is very general as it represents a class of distribution‐free control charts based on distances. Numerical results show that the proposed control chart is efficient in detecting mean shifts in both symmetric and heavy‐tailed distributions.