Circular Error Probabilities

A problem which often arises in connection with the determination of probabilities of various miss distances of bombs and missiles is the following: Let x and y be two normally and independently distributed orthogonal components of the miss distance, each with mean zero and with standard deviations σ x and σ y , respectively, where for convenience one labels the components so that σ x ≥σ y . Now for various values of c = σ y /σ x , it is required to determine (1) the probability P that the point of impact lies inside a circle with center at the target and radius Kσ x , and (2) the value of K such that the probability is P that the point of impact lies inside such a circle. Solutions of (1), for c = 0.0(0.1) 1.0 and K = 0.1 (0.1) 5.8, and (2), for the same values of c and P = 0.5, 0.75, 0.9, 0.95, 0.975, 0.99, 0.995, 0.9975, and 0.999, are given along with some hypothetical examples of the application of the tables.