The problems studied here may seem unrelated, although the analysis of each requires the use of the circular coverage function. The first considers an n-weapon attack on a circular area with uniform target density; the damage function is based on Hunter's (1967). The second considers a single-weapon attack on a target area with a symmetric normal density of targets, using a generalized 'cookie-cutter' damage function. The damage functions used are believed to provide better fits to certain empirical damage curves than the cookie-cutter, and they have not previously been studied with the target models here. Algorithms are derived for calculating the expected number of casualties, or of targets damaged. Symmetric Gaussian aiming errors are assumed in both problems
Two Casualty-Estimation Problems Associated with Area Targets and the Circular Coverage Function
Read, CB. (1971). Two Casualty-Estimation Problems Associated with Area Targets and the Circular Coverage Function. Operations Research, 19(7), 1730-1741.