Damage accumulation and probability of kill for gun and target engagements

• Published in: Naval research logistics Vol. 65; no. 2; pp. 160 - 175
• Main Authors: Chircop, Paul A., Kachoyan, Bernard J.
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc 01.03.2018
• Subjects: Accumulation; Conditional probability; Damage accumulation; discrete gamma distribution; Distribution; Gunfire; Mathematical models; Modelling; Parameters; Probability distribution; probability of kill; probability of kill given hit; Probability theory; Production methods; Vulnerability
• ISSN: 0894-069X; 1520-6750
• DOI: 10.1002/nav.21784

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.