Some Weapon System Survival Probability Models—II. Random Time Between Firings

Part II of this study centers about mathematical models in which the number of times a weapon system fires during a time interval of length t is assumed to be random and given by a Poisson distribution with parameter λt where λ is the average rate of fire. The single-shot kill probabilities are permitted to be time dependent—an increasing kill probability reflecting the effect of improved target location, a decreasing kill probability indicating possible movement of the target. Still other interpretations are possible. In another model the friendly force is permitted to evacuate, its position after evacuation being a random variable. In this model the distance that the friendly force moves in time t is assumed to be given by a Rayleigh distribution with parameter λ_t, which is a function of time. The possible tradeoff between increased numbers of weapon systems and greater surveillance capability is indicated. Lifetime distributions and other quantities of interest are obtained for both the friendly and the enemy force.