Operating characteristics of X-bar charts with asymmetric control limits

Abstract

When the assumptions behind the Shewhart chart are not met, policies other than the traditional 3-sigma limits may enable speedier and more economical detection of process change. If a process has unequal probabilities of downward and upward shifts, downward shifts of differing magnitude from upward shifts, and/or standard deviations after downward shifts different from those after upward shifts, then increases in the in-control average run length and decreases in the out-of-control average run length are simultaneously achievable with control limits placed at unequal distances from the process mean. The magnitude of these improvements is investigated for several types of process. The results are then extended to median charts for processes with output that is not normally distributed.

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