Tables of Run Length Percentiles for Determining the Sensitivity of Shewhart Control Charts for Averages with Supplementary Runs Rules

Abstract

Shewhart control charts for averages are sometimes used to detect shifts in the process mean for feedback control or for the monitoring of the distribution of a measurement made on outgoing product. The sensitivity of a chart to a process mean shift is measured by the distribution of the run length, that is, the number of chart points after the shift that a signal is given on the chart that the shift has occurred. This study provides the practitioner with tables of the percentile values of this distribution and gives some examples of their use, including the evaluation of subgroup size with a fixed sampling rate and the rate of false alarms.