The economic design of an (X)over-bar control chart recognizing process improvement

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.