Application of copulas to multivariate control charts

• The method presented is inspired by the density level set estimation approach.
• We propose to use copulas in order to model the multivariate distribution.
• The tolerance region is constructed such as the probability of false alarm is equal to αα.

The most popular multivariate control chart for monitoring the mean of a distribution is probably the Hotelling T2 rule. Unfortunately, this rule relies on the assumption that the distribution under control is Gaussian, which is rarely true in practice. The objective of this paper is to propose a new approach for the non-normal multivariate case. It consists in the construction of a tolerance region obtained from a density level set estimation. The method follows a “plug-in” approach in which the density of the observations is previously estimated. This estimation is conducted using copulas modeling, an increasingly popular tool in multivariate modeling.