Monitoring a Poisson process in several categories subject to changes in the arrival rates

We look at a Poisson process in several categories where the arrival rate changes at some unknown integer. For some of these categories the arrival rates increase, while in other categories the arrival rates decrease. The point at which the process changes may be different for each category. We develop procedures for detecting when a change has occurred in at least one of the categories. We provide some numerical results to illustrate the effectiveness of the detection procedures.