Notes on Firing Theory
Abstract : These notes are intended to be tutorial in nature, rather than comprehensive. The reader who desires a comprehensive treatment should see 1, which contains additional references to the considerable literature that exists on "coverage problems." It seems to be the nature of the subject that there are a great many conceptually similar cases and sub-cases, each requiring a different mathematical treatment. Our goal here is to describe and summarize the main ideas, recording in the process only those results for which simple expressions are available. The material in the first three sections of these notes is devoted to computations of the probability of "killing" a target with possibly several "weapons", with the effectiveness of each weapon depending on a two-dimensional miss distance. The same mathematics applies to computations of such things as the probability of "detecting" a target with "sensors"; the only essential feature is that the crucial event must either happen or not. Partial damage is not permitted - each shot either kills the target or leaves it unscathed. This assumption is often not realistic, but it nonetheless must serve because practically all analysis is based on it.