Simultaneous monitoring of process mean vector and covariance matrix via penalized likelihood estimation

In recent years, some authors have incorporated the penalized likelihood estimation into designing multivariate control charts under the premise that in practice typically only a small set of variables actually contributes to changes in the process. The advantage of the penalized likelihood estimation is that it produces sparse and more focused estimates of the unknown population parameters which, when used in a control chart, can improve the performance of the resulting control chart. Nevertheless, the existing works focus on monitoring changes occurring only in the mean vector or only in the covariance matrix. Stemming from the ideas of the generalized likelihood ratio test and the multivariate exponentially weighted moving covariance, new control charts are proposed for simultaneously monitoring the mean vector and the covariance matrix of a multivariate normal process. The performance of the proposed charts is assessed by both Monte-Carlo simulations and a real example.