Variable sampling interval hotelling's T2 charts with runs rules for switching between sampling interval lengths

The use of runs rules is proposed for switching between the sampling interval lengths of variable sampling interval Hotelling's T2 charts. The purpose of applying these rules is to reduce the frequency of the switches which causes inconvenience in the administration of the charts. The expressions for the performance measures for the charts with these rules are derived. The effects of different runs rules on the performances are evaluated through numerical comparisons. The runs rules substantially reduce the frequency of switches during the in-control period and during the out-of-control periods due to the small to moderate shifts in the process mean vector. They also fairly improve the statistical performances of the charts in detecting the small shifts and do not affect that in detecting the large shifts. However, some runs rules slightly worsen the statistical performances in detecting the moderate shifts. Copyright (c) 2011 John Wiley & Sons, Ltd.