On the distribution of the T2 statistic, used in statistical process monitoring, for high-dimensional data

A modification to the asymptotic distribution of the T-2-statistic used in multivariate process monitoring is provided when the dimension of the vectors may exceed the sample size. Under certain mild condition, a unified limit distribution is obtained that is applicable for both Phase I and II charts. Further the limit holds for charts based on individual observations as well as subgroup means. The limit is easily applicable and does not need any data preprocessing or dimension reduction. Simulations are used to demonstrate the accuracy of the proposed limit. (C) 2020 Elsevier B.V. All rights reserved.