Optimum Search for Objects Having Unknown Arrival Times

Nelson Blachman and Frank Proschan
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Nelson Blachman: Electronic Defense Laboratory, Sylvania Electric Products, Inc., Mountain View, California
Frank Proschan: Electronic Defense Laboratory, Sylvania Electric Products, Inc., Mountain View, California

Operations Research, 1959, vol. 7, issue 5, 625-638

Abstract: In defense against missiles, early detection is crucial. This is the motivation for the mathematical solution of the following general search problem. Objects arrive in accordance with a Poisson process. Having arrived, the object appears (and remains until detected) in box i with probability p i . A single scan of box i costs Ci (possibly including the cost of false alarms), takes time t i , and, if the object is present in box i at the beginning of the scan, will detect it with probability Pi . The resultant gain g i ( t ) is a nonincreasing function of t , the delay between arrival and the beginning of the detecting look, i = 1, 2, ..., n . An asymptotically optimum search procedure is obtained. A number of particular cases of interest are solved.

Date: 1959
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