Optimal investigating search maximizing the detection probability

In this paper, we deal with a two-stage search consisting of the broad search and the investigating search, and derive conditions of an optimal investigating search plan maximizing the detection probability of a target. We consider a search for a target in an area under a restriction of search time. In this search, contacts of false signal caused by system noise are inevitable, and when a contact is gained, the searcher must investigate the contact to ascertain whether it is the true target or not. We derive conditions of the optimal investigating time and elucidate properties of the optimal plan. Several numerical examples are examined and interpretations of the optimal conditions are given.