  The problem of quickest detection of an anomalous process among M processes
is considered. At each time, a subset of the processes can be observed, and the
observations from each chosen process follow two different distributions,
depending on whether the process is normal or abnormal. The objective is a
sequential search strategy that minimizes the expected detection time subject
to an error probability constraint. This problem can be considered as a special
case of active hypothesis testing first considered by Chernoff in 1959 where a
randomized strategy, referred to as the Chernoff test, was proposed and shown
to be asymptotically (as the error probability approaches zero) optimal. For
the special case considered in this paper, we show that a simple deterministic
test achieves asymptotic optimality and offers better performance in the finite
regime. We further extend the problem to the case where multiple anomalous
processes are present. In particular, we examine the case where only an upper
bound on the number of anomalous processes is known.
