Distribution-free multivariate process monitoring: a rank‐energy statistic‐based approach

In this paper, a multivariate process monitoring scheme based on the rank‐energy statistics is proposed which is suitable for high‐dimensional applications such as sensorless drive diagnosis. The rank‐energy statistic is based on multivariate ranks that is grounded on the measure transportation theory. Univariate ranks could be interpreted as a solution to an optimisation problem involving a given set of observations of size n $n$ and the set { 1 , 2 , 3 , . . , n $1,\ 2,\ 3,..,\ n$ }. Recently, attaining greater robustness than spatial sign or depth‐based ranks, multivariate ranks are proposed as solutions to such optimisation problem in multivariate settings (measure transportation problem). The proposed multivariate process monitoring scheme based on the rank‐energy statistic, subsequently, attains greater robustness than existing nonparametric multivariate process monitoring methods based on spatial sign or depth‐based ranks. The proposed method is also applicable to high‐dimensional data unlike some of the existing nonparametric multivariate process monitoring methods. A rigorous simulation study demonstrates its effective shift detection ability and other important features. A practical application of the proposed method is demonstrated with the sensorless drive diagnosis case study.