An Optimal Control Procedure based on Multivariate Synthetic Cumulative Sum

A multivariate synthetic cumulative sum (MSCUSUM) control chart is presented in this study. The MSCUSUM control chart consists of a multivariate cumulative sum (MCUSUM) control chart and a conforming run length (CRL) control chart, and it combines the strengths of both cumulative sum and CRL procedures. Some properties of this new scheme are investigated, and implementation procedure is shown with real data example. Simulation studies are also carried out to show that the MSCUSUM control chart is more efficient than the MCUSUM, synthetic T² and Hotelling's T² control charts, for detecting shifts in the process mean vector. The MSCUSUM chart also performs slightly better than the multivariate synthetic exponentially weighted moving average chart in detecting moderate and large shifts.