Solving the combinatorial explosion problem when calculating the multiple-hit vulnerability of aircraft

Two precise calculation methods (Markov chain or tree diagram) are commonly used for assessing aircraft vulnerability to multiple hits by nonexplosive penetrators. Because the dimension of Markov transition matrix or the number of tree branches increases exponentially along with the increasing number of redundant components, when the total number of redundant components reaches a certain amount, the "combinatorial explosion" is unavoidable. This paper, using the Monte Carlo technique, proposes a method for solving the combinatorial explosion problem. This method simulates all of the existing states of aircraft to Model of Filling Boxes with Balls; by randomly and uniformly sampling the threat hit locations, the aircraft cumulated probability of kill can be attained. Two provided examples show the correctness and feasibility of the proposed method. Analysis shows that the developed method with high accuracy apparently costs a short amount of time compared with the precise methods, when the total number of the redundant components is relatively large. Moreover, the CPU run time increases almost linearly along with the increasing number of redundant components, and the combinatorial explosion is avoided, and so this method is more applicable to engineering computation.