Detection of an unknown increase in the rate of a rare event

Abstract

Control charts for detecting shifts in the rate of occurrences of rare events are usually implemented by fixing a priori the change to be optimally detected, i.e. under the assumption that the change is from a baseline in-control value to a known out-of-control value. In practice, this assumption is never satisfied. A solution to that problem, mainly devoted to the real world of continuous surveillance, is developed here in terms of a natural extension of the minimizing out-of-control averge run length (ARL) criterion. As an illustrative application, the procedure is analytically solved for the exponential Sets charts. In this case, exact numerical tables of the expected out-of-control ARL, based on the proposed criterion, are also given.