On Assessing the Performance of Sequential Procedures for Detecting a Change

The literature on statistical process control has focused mostly on the average run length (ARL) to an alarm, as a performance criterion of sequential schemes. When the process is in control, this is the ARL to false alarm, generally denoted by ARL0, and represents the in‐control operating characteristic of the procedure. The ARL from the occurrence of a change to its detection represents an out‐of‐control operating characteristic and is typically embodied by ARL1, the ARL to detection assuming that the change occurs at the very start of surveillance. However, these indices do not tell the whole story, and at times they are not defined well by a single number. We review the role of various operating characteristics in assessing performance of sequential procedures in comparison with ARL0 and ARL1.