The Rate of False Signals in Ū Control Charts with Estimated Limits

The in-control statistical properties of Ū charts have usually been studied from the perspective of the average run length (ARL) until the first (false) signal, known as the in-control ARL. We argue that the ARL is a confusing concept when used with charts with estimated limits and that the rate of false signals (RFS), which focuses on the behavior of charts during extended use, is more intuitive. We use the RFS to illustrate graphically the dangers of using too few subgroups to estimate control limits. We also discuss diffidence charts, which make the inherent uncertainty concerning RFS observable to the practitioner and thus help the practitioner determine what is an acceptable number of subgroups for a given charting application.