X̅ Charts with Variable Control and Warning Limits

Abstract Adaptive control charts deliver significantly better performances than that of static control charts. However, the frequent switches between sampling interval lengths and/or between sample sizes can be a complicating factor in the administration of these charts. This factor is totally absent for the adaptive chart proposed in this paper. The proposed chart is an X̅ chart with variable control and warning limits (VCWL). Expressions for the performance measures for this chart are developed. The methods presented are general and can be applied to other Shewhart control charts. The performances of VCWL X̅ charts are compared numerically with that of static X̅ charts. It is observed that the idea of VCWL significantly improves the performances of X̅ charts in detecting small to moderate shifts in the process mean without affecting that in detecting large shifts.