The design of the multivariate synthetic - T 2 control chart

One of the objectives of the research done in statistical process control is to obtain control charts that show few false alarms but, at the same time, are able to detect quickly the shifts in the distribution of the quality variables employed to monitor a productive process. In this paper the synthetic-T control chart is developed, which consists of the simultaneous use of a CRL chart and a Hotelling’s T control chart. A procedure of optimization has been developed to obtain the optimum parameters of the synthetic-T, given the values of in-control ARL and magnitude of shift which needs to be detected rapidly. The comparison versus the charts MEWMA, T with variable simple size and T with double sampling shows that the synthetic-T chart always performs better than the standard T chart. The comparison with the remaining charts reveals in which cases the performance of this new chart makes it interesting to employ in real applications.