The economic design of a flexible zone X¯-chart with AT&T rules

Duncan's economic design of Shewhart's X¯-control chart has established its optimal design for monitoring a process. Recently, there has been a renewed interest in the use of supplementary runs rules to increase the sensitivity of the chart to small shifts. This paper presents: (1) a general version of Duncan's model in that AT&T rules 1 and 2 or AT&T rules 1, 2, and 3 are used, and (2) a flexible-zone methodology in that the zone widths are not fixed a priori but are determined by economic optimization on the basis of the particular situation at work. It is observed that the use of AT&T rules with economic design can result in substantial cost savings over Duncan's design for small shifts in the process average.

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