In this paper we consider the use of an (X) over bar-chart for controlling
a single-stage process. The three controllable variables, as usual, are the
interval between consecutive samples, the sample size, and the distance aw
ay from the in-control process mean at which the control limits are placed.
Costs considered are those of sampling, false alarms, operating when the p
rocess is out-of-control, and identification of underlying causes/putting p
rocess back in control. Most importantly, we take account of process improv
ement (reduction in the frequency of out-of-control situations) as causes a
re determined and possibly eliminated. An optimal procedure for dynamically
setting the values of the three control parameters is presented and compar
ed over a wide range of numerical examples with two simpler approaches. The
re are substantial cost savings associated with taking account of process i
mprovement.