Dual multivariate CUSUM mean charts

The multivariate CUSUM (MCUSUM) chart can be optimally designed to detect a specific shift in the process mean. In practice, the shift size is rarely known but it is known that it varies within a given interval. Thus, the MCUSUM chart may not perform well when detecting a range of the mean shift sizes. To overcome this issue, in this paper, we propose new dual MCUSUM (DMCUSUM) and mixed DMCUSUM (MDMCUSUM) charts for monitoring the mean of a multivariate normal process. The DMCUSUM (MDMCUSUM) chart integrates two similar (different) type MCUSUM charts into a single chart to provide an overall good detection for different sizes of shift in the process mean. The run length characteristics of these DMCUSUM charts are computed using the Monte Carlo simulation method. A detailed comparative study of the proposed and existing multivariate charts in terms of the average run length (ARL), extra quadratic loss and integral relative ARL is shown to be favorable to the former. Two real datasets are considered to explain the implementation of the proposed multivariate charts.