Setting Control Limits in a Multivariate Exponentially Weighted Moving Likelihood Control Chart

A control chart is one of the representative methodologiesused in statistical process control. A multivariate control chart is used todetect changes in multiple variables. Ueno and Nagata (2018) proposed amultivariate exponentially weighted moving likelihood (MEWML) control chartaimed at detecting minor changes in the mean vector and variance-covariancematrix. Although the MEWML control chart can accurately detect the change whenthe variance increases, it is unable to detect the change when it decreases. Areduction in variance implies that the procedure is moving to a better state.Therefore, detecting the change can lead to an improvement in the procedure. Inthis paper, we detect reductions in variance by considering both the upper andlower control limits. Through a simulation, we demonstrate that reduction invariance can be detected by using the lower control limit.