A simple stochastic model of air-naval combat

Consideration is given to a scenario where a fleet of ships, each armed with the same anti-aircraft weapon, is attacked by identical aircraft in line-ahead formation. It is assumed that each aircraft uses its weapon against one ship, but all ships use their weapons against each aircraft as it attacks in turn. A difference equation for the bivariate probability distribution of ship and aircraft casualities is obtained, and some analytic results are derived by decomposition of the problem. Using data from the sinking of the HMS Prince of Wales and HMS Repulse in World War II to estimate parameter values, a numerical solution of the difference equation is provided. A separate method for computing the ultimate or terminal form of the distribution is given.