Quickest Search for a Change Point

Javad Heydari, Ali Tajer

Abstract: This paper considers a sequence of random variables that undergo periods of transient changes at an unknown set of time instants, referred to as transient change-points. The objective is to constantly monitor the sequence in order to detect one of the change-points subject to a hard constraint on the detection delay, while in parallel, the rate of false alarms is controlled. This setting is fundamentally different from the conventional change-point detection problems, in which there exists at most one change-point that can be either persistent or transient. In this paper, the exact optimal decision rules are characterized. Furthermore, it is shown that in the special case that the objective is detecting a transient change-point at exactly the instant that a change occurs (i.e., no detection delay), the test reduces to the well-known Shewhart test. Numerical evaluations are also provided to assess the performance of the decision rules.