Mean Action Time of the <i>X</i> Control Chart with Warning Limits

Abstract

The Shewhart control chart for means can be made more sensitive to small changes by adding a pair of warning limits, located inside the action limits, and taking action when a run of a specified number of consecutive means falls between the warning and action lines. Sensitivity is measured by the mean action time (M.A.T.) as function of the shift in the mean of the process. This paper discusses in detail the individual and combined effects upon the level and shape of the M.A.T. functions, of changes in the location of the action and warning limits and the critical run length. Great flexibility in parameter selections yields charts that give much larger M.A.T.'s when the process is in control, yet will detect shifts of certain magnitudes more rapidly than Shewhart charts.