Monitoring a Poisson process subject to gradual changes in the arrival rates where the arrival rates are unknown. Issue 3 (3rd July 2021) - Brown, Marlo
Abstract: We look at a Poisson process where the arrival rates change from λ 1 to λ 2 . We will assume that the arrival rates both before and after the change are unknown. We also assume that this change does not happen abruptly but gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop early.