CUSUM Schemes for Stationary and Nonstationary Gaussian Processes

In the paper, we derive two types of the multivariate CUSUM control charts for stationary and variance nonstationary Gaussian processes based on maximizing the generalized likelihood ratio. As partial cases, the control schemes for independent observations and autoregressive processes are obtained. The second application leads to the two multivariate CUSUM control charts when the covariance matrix is separable. We show that the proposed schemes possess the invariance property. The performance of the control charts is studied within a simulation study.