On constructing T^2 control charts for on-line process monitoring

In this paper we study the performance of x ^2 control limits on T ^2 control charts during on-line process monitoring. We make recommendations on the minimum number of subgroups necessary for control charts based on estimated parameters to perform similar to control charts based on true parameters when the x ^2 control limit is used. We discuss an exact procedure for constructing T ^2 control charts using estimated parameters that perform similar to control charts based on true parameters regardless of the number of preliminary subgroups. Furthermore, we suggest an implementation approach for using Altʹs control limit on T ^2 control charts until the accumulation of recommended minimum number of subgroups.