  We consider the problem of sequential detection of a change in the
statistical behavior of a hidden Markov model. By adopting a worst-case
analysis with respect to the time of change and by taking into account the data
that can be accessed by the change-imposing mechanism we offer alternative
formulations of the problem. For each formulation we derive the optimum
Shewhart test that maximizes the worst-case detection probability while
guaranteeing infrequent false alarms.
