Improved control chart performance using cautious parameter learning

Parameter estimation is an important topic in Statistical Process Monitoring, as inaccurate estimates may lead to undesirable control chart performance. Updating the control chart limits during the monitoring period reduces estimation uncertainty. However, when out-of-control situations remain undetected, using the corresponding samples to update the parameter estimates can deteriorate the control chart performance in terms of in-control and out-of-control run lengths. For this reason, updating parameter estimates should only occur when there is sufficient evidence of an in-control process state. In this article, we study the performance of a cautious updating scheme for the Shewhart, Cumulative Sum, and Exponentially Weighted Moving Average control charts. We propose simple rules for updating parameters that improve the out-of-control performance of the control charts. We show the added value of using these updating rules in practice through a case study using data from a truck manufacturer.