The effect of continuously updating control chart limits on control chart performance

An open topic within statistical process monitoring is the effect on control chart properties of updating the control chart limits during the monitoring period. The challenge is to use the correct data for updating the control limits as in‐control data could be incorrectly classified as out of control and therefore not used for re‐estimating the parameters, and out‐of‐control data could be classified as in control and therefore used for re‐estimating. In the present article, we study the effect of updating the Shewhart, cumulative sum, and exponentially weighted moving average control chart limits. We simulate different scenarios: the monitoring data could be in or out of control, and the practitioner may or may not be able to find out whether the process is indeed out of control when the control chart gives a signal. The results reveal that the variation in the performance of the conditional control charts decreases significantly as a result of updating the control chart limits when the updating data are in control and also when the updating data are out of control and the practitioner is able to classify correctly data samples that produce a signal. However, when a practitioner is not able to classify a signal correctly, the advisability of updating depends on the type of control chart and the level of data contamination.