Analytic Expressions for the Probability of Penetrating a Point Defense

A method is developed for computing the probability that an air attack will penetrate a point defense made by a surface-to-air missile system. Analytic expressions are obtained from a model for the probability of penetration by at least one of k attackers, as a function of k and of the spacing between successive attackers, the number of shots that can be made at an approaching attacker, and the single-shot kill probability of the defensive missiles. The mean number of attackers required for penetration can be approximated very closely by a formula that is valid throughout the range of tactical interest.