Guaranteed in-control control chart performance with cautious parameter learning

Parameter estimation has a large impact on control chart performance. Recently, widened control limits have been suggested to guarantee an acceptable in-control behavior. However, the consequence is a reduced ability to detect a real change in the process. In order to overcome this undesired effect, we explore an alternative design based on a delayed updating of parameter estimates. We consider an application to the Shewhart X, EWMA, and CUSUM control charts for the process mean. This approach is simple to implement, reduces the variation of the in-control average run lengths, and significantly improves the out-of-control performance.