Classical Versus Short-Run X Charts
Gregory E. Rahn · 1995
Abstract Although accurate short-run control charts have been established to account for the variability associated with the parameter estimates, quality control practitioners have been reluctant to abandon classical X̄ charts because clear differences have not been demonstrated to overcome the inertia of changing control chart methodologies. This paper focuses on the consequences of instituting classical X̄ chart limits on short-run processes under the two phases of control: “control with no standard given” and “control with respect to a given standard”. Specifically, the biased probability of a false alarm is derived when classical limits are enforced and is compared to the known probability (.0027) that is exhibited from the short-run chart. The probability of one or more false alarms when monitoring multiple subgroups over time is also examined. Ironically, the bias resulting in inflated false alarm rates was most visible when monitoring under “control with respect to a given standard”, which has been the preferred choice of control because of its real-time capability. Fortunately, the accuracy of short-run charts is guaranteed regardless of the sampling condition or monitoring phase.