On the Computation of Hit Probability

Abstract

Computing the accuracy with which guns and similar weapon systems deliver ordnance is, in its most general context, a problem in the theory of discrete stochastic processes. Thus, the classic methods of computing hit probability by assuming the impact points to be isolated random variables are much too restrictive to be of general use. As a result, there exists in the literature a profusion of formulas, tables, and computational methods whose applications are limited to a variety of special cases. This in itself is no handicap as long as a unifying theory exists from which all these special cases follow. However, it is precisely the lack of such a theory that has made the available results ambiguous, confusing, and generally unsatisfying. The aim of this paper is to remedy this situation by providing a theoretical framework for the concise definition of hit distribution and its computation. The subjects treated are the various types of errors inherent in gun systems, and a general discussion of hit distribution and its computation, as well as a detailed analysis of independent and Markov-dependent rounds and the diffuse-target approximation.