Nonparametric multivariate statistical process control charts: a hypothesis testing-based approach

Abstract

Nonparametric multivariate control charts are highly sought-after due to their flexibility to adapt to different distribution assumptions. However, most existing nonparametric multivariate control charts involve some tuning parameter, which needs to be pre-specified to implement those control charts. To choose the appropriate tuning parameter to achieve optimal performance, it usually requires the information about the out-of-control distribution. However, in practice, it is rarely known in advance what the out-of-control distribution is. In this paper, we propose a new nonparametric multivariate phase-II control chart using a hypothesis testing-based approach when a body of reference data (phase-I data) is available. The proposed control chart does not depend on any tuning parameter, and can be considered as a natural generalisation of the generalised likelihood ratio chart to the nonparametric setting. Our simulation study and real data analysis show that the proposed control chart performs well across a broad range of settings, and compares favourably with existing nonparametric multivariate control charts.