Implementation copula to multivariate control chart

Abstract

Multivariate Control Chart is an effective tool in Statistical Process Control to identify either an out-of-control process or in-control process. Hotelling T2 control chart is a quite popular and widely used technique in this field. However, its performance is deteriorated when the underlying distribution of the quality characteristics is not following the multivariate normal distribution. Multivariate control chart usually recommends a procedure in the phase-in Hotelling T2 control chart although there is difficulty in interpreting the signals from multivariate control charts more work is needed on data reduction methods and graphics techniques. Basically, the multivariate control chart refers to the theory of prediction interval. Therefore, it’s called predictive multivariate control charts. The purpose of this research is to construct what so-called predictive multivariate control chart both classical in this part in the phase-in Hotelling T2 and Copula-based ones. We argue that appropriate joint distribution function may be well estimated by employing Copula. A numerical analysis is carried out to illustrate that an Application Copula-based Multivariate control chart outperforms than bivariate control chart and others.