Control charts for health care monitoring under intermittent out-of-control behavior

Health care monitoring typically concerns attribute data with very low failure rates. Efficient control charts then signal if the waiting time till r (e.g. r≤5) failures is too small. An interesting alternative is the MAX-chart, which signals if all the associated r waiting times for a single failure are sufficiently small. In comparing these choices, the usual change point set-up has been used, in which going Out-of-Control (OoC) means that the failure rate suddenly jumps up and then stays at this higher level. However, another situation of interest is intermittent OoC behavior. In industrial settings, an OoC process can be adjusted to return to In-Control (IC), but with health care monitoring this usually is no option and stretches of OoC and IC behavior may alternate. Comparison of such intermittent alternatives to the change point situation shows that the former can be characterized as tail alternatives, in the sense that the difference w.r.t. the IC-distribution becomes more concentrated in the lower tail. This suggests to generalize the MAX-chart as follows: now signal if all but 1 (or 2) out of r individual waiting times are too small. A numerical study shows that this approach indeed works well.