  This paper considers a sequence of random variables generated according to a
common distribution. The distribution might undergo periods of transient
changes at an unknown set of time instants, referred to as change-points. The
objective is to sequentially collect measurements from the sequence and design
a dynamic decision rule for the quickest identification of one change-point in
real time, while, in parallel, the rate of false alarms is controlled. This
setting is different from the conventional change-point detection settings in
which there exists at most one change-point that can be either persistent or
transient. The problem is considered under the minimax setting with a
constraint on the false alarm rate before the first change occurs. It is proved
that the Shewhart test achieves exact optimality under worst-case change points
and also worst-case data realization. Numerical evaluations are also provided
to assess the performance of the decision rule characterized.
