Hotelling’s T2 charts with variable sample size and control limit

The ideas of variable sampling interval (VSI), variable sample size (VSS), variable sample size and sampling interval (VSSI), and variable parameters (VP) in the univariate case have been successfully applied to the multivariate case to improve the efficiency of Hotelling’s T2 chart with fixed sampling rate (FSR) in detecting small process shifts. However, the main disadvantage in using most of these control schemes is an increasing in the complexity due to the adaptive changes in sampling intervals. In this paper, retaining the lengths of sampling intervals constant, a variable sample size and control limit (VSSC) T2 chart is proposed and described. The statistical efficiency of the VSSC T2 chart in terms of the average time to signal a shift in process mean vector is compared with that of the VP, VSSI, VSS, VSI, and FSR T2 charts. From the results of comparison, it shows that the VSSC T2 chart for a (very) small shift in the process mean vector gives a better performance than the VSSI, VSS, VSI, and FSR T2 charts; meanwhile, it presents a similar performance to the VP T2 chart. Furthermore, from the viewpoint of practicability, it is more convenient for administrating the control chart than the VSI, VSSI, and VP T2 chart. Thus, it may provide a good option for quick response to small shifts in a multivariate process.