A robust multivariate EWMA control chart for detecting sparse mean shifts

In multivariate statistical process control (MSPC) applications, process mean shifts sometimes occur in only a few components. To solve this MSPC problem, many control charts were proposed in the literature. Most of these charts assumed that the multivariate quality characteristics are normally distributed. Among them, the control chart proposed by Zou and Qiu (2009), incorporating the least absolute shrinkage and selection operator (LASSO) method into the EWMA scheme, has the best overall performance. In this paper, we extend the classical multivariate LASSO control chart to a robust version that has an affineinvariance property and is distribution free under the family of elliptical direction distributions, indicating that the in-control run-length distribution is the same for any continuous distribution in this family and the control limit can be acquired from the multivariate standard normal distribution. Our simulation results show that the proposed method is very efficient in detecting various sparse shifts under heavy-tailed and skewed multivariate distributions. In addition, it is easy to implement with an iterative algorithm and the least angle regression (LARS) algorithm. White-wine data illustrates that the proposed control chart performs quite well in applications.