On Optimal Aiming to Hit a Linear Target

Typically weapon systems have an inherent systematic error and a random error for each round, centered around its mean point of impact. The systematic error is common to all aimings. Assume such a system for which there is a preassigned amount of ammunition of n rounds to engage a given target simultaneously, and which is capable of administering their fire with individual aiming points (allowing "offsets"). The objective is to determine the best aiming points for the system so as to maximize the probability of hitting the target by at least one of the n rounds. In this paper we focus on the special case where the target is linear (one-dimensional) and there are no random errors. We prove that as long as the aiming error is symmetrically distributed and possesses one mode at zero, the optimal aiming is independent of the particular error distribution, and we specify the optimal aiming points. Possible extensions are further discussed, as well as civilian applications in manufacturing, radio-electronics, and detection.