Damage accumulation and probability of kill for gun and target engagements

Abstract

Determination of the gunfire probability of kill against a target requires two parameters to be taken into consideration: the likelihood of hitting the target (susceptibility) and the conditional probability of kill given a hit (vulnerability). Two commonly used methods for calculating the latter probability are (1) treating each hit upon the target independently, and (2) setting an exact number of hits to obtain a target kill. Each of these methods contains an implicit assumption about the probability distribution of the number of hits-to-kill. Method (1) assumes that the most likely kill scenario occurs with exactly one hit, whereas (2) implies that achieving a precise number of hits always results in a kill. These methods can produce significant differences in the predicted gun effectiveness, even if the mean number of hits-to-kill for each distribution is the same. We therefore introduce a new modeling approach with a more general distribution for the number of hits-to-kill. The approach is configurable to various classes of damage mechanism and is able to match both methods (1) and (2) with a suitable choice of parameter. We use this new approach to explore the influence of various damage accumulation models on the predicted effectiveness of weapon-target engagements. K E Y W O R D Sdamage accumulation, discrete gamma distribution, probability of kill, probability of kill given hit, vulnerability Naval Res Logistics. 2018;00:1-17. wileyonlinelibrary.com/journal/nav