THE SWITCHING BEHAVIOR OF (X)OVER-BAR CHARTS WITH VARIABLE SAMPLING INTERVALS

In a variable sampling interval control scheme the time interval between successive samples is allowed to vary depending on what is being observed from the data. It has been the practice to compare the average time to signal and the average run length of variable sampling interval schemes and the corresponding control procedures with fixed sampling intervals. Thus far design tables for control charts with variable sampling intervals have not considered the effect of the design parameters on the switching behavior of such control procedures. Frequent switches between the different sampling intervals can be a complicating factor in the application of control charts with variable sampling intervals. The problem of switches is addressed in this article and improved switching rules are presented and evaluated for Shewhart control procedures. Expressions for the average number of switches and the average time to signal are obtained. The proposed runs rules considerably reduce the average number of switches between the sampling intervals and improve the efficiency of the XBAR chart.