SB-robustness of performance measures of control chart

Abstract

Control charts play a very important role in the control of manufacturing processes. In this paper we consider the commonly used performance measures for control charts and study their SB-robustness. It is shown that the False Alarm Probability, Average Sample Number (ASN) when the process is in-control, No-Signal Probability and ASN when the process is out-of-control are all SB-robust at the family of all normal distributions with bounded mean and standard deviation. It is also shown that these performance measures are not SB-robust at the larger family of normal distributions with unbounded mean and standard deviation.