Multivariate triple sampling Hotelling's T2 control chart

Multivariate process control has recently gained significant attention because it takes into account the correlation between process variables and offers a more comprehensive understanding of the overall process behavior. In line with this phenomenon, this paper proposes the multivariate triple sampling Hotelling's T-2 (MTS) control chart as an efficient process monitoring method in multivariate statistical process control. The mathematical properties of the MTS chart are also derived. The performance of the MTS chart is assessed using key performance metrics, such as average run length (ARL), average number of observations to signal (ANOS) and expected average number of observations to signal (EANOS). The performance of the MTS chart is compared with that of the existing multivariate double sampling Hotelling's T-2 (MDS) chart. The findings indicate that the MTS chart consistently surpasses the MDS chart across all performance metrics, demonstrating its superior capability in detecting shifts for a multivariate process. Notably, the MTS chart exhibits lower ARL, ANOS and EANOS values, emphasizing its effectiveness in promptly identifying process shifts. In terms of practical application, an example is given to elucidate the execution of the MTS chart.