The Design and Performance of the Multivariate Synthetic-T2 Control Chart

One of the objectives of research 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 article, the synthetic-T2 control chart is developed, which consists of the simultaneous use of a CRL chart and a Hotelling's T2 control chart. The ARL is calculated employing Markov chains for steady and zero-state scenarios. A procedure of optimization has been developed to obtain the optimum parameters of the synthetic-T2, for zero and steady cases, given the values of in-control ARL and magnitude of shift which needs to be detected rapidly. A comparison between (standard T2, MEWMA, T2 with variable sample size, and T2 with double sampling) charts reveals that the synthetic-T2 chart always performs better than the standard T2 chart. The comparison with the remaining charts demonstrate in which cases the performance of this new chart makes it interesting to employ in real applications.