A Survey of Coverage Problems Associated with Point and Area Targets

At first glance the subject-matter of this paper may appear to be rather trivial. No questions of offense or defense strategies are involved; one is interested solely in calculating the probability that a point target is destroyed by one or more weapons in a salvo. If the target, has an extended area, the probability of destruction is replaced by the expected fraction of the target destroyed. One might reasonably conclude that a few simple mathematical arguments involving independent random events are all that is required. However, appearances are deceptive. Since the second world war a large number of authors have dealt with problems of this type and the results of their researches are widely scattered through the mathematical literature under the general name of coverage problems. A few answers can be obtained in closed form, but the majority run into diffkulties which can be overcome only by numerical integration or simulation. This paper attempts to classify these researches into a more-or-less logical pattern, emphasizing ideas and results rather than derivations. This paper is written for the engineer rather than the mathematician. Specifically, it is restricted to two-dimensional coverage problems rather than n-dimensional ones. Furthermore, little if any attention is given to that part of the literature which deals with the mathematical properties of various probability density functions useful in coverage problems. The reader interested in these details is referred to Ruben (1960). Part of the material in this survey is discussed in two excellent review articles on coverage problems by Guenther and Terragno (1964) and Guenther (1966).