A New Formulation of Lanchester Combat Theory

Lanchester's differential equations of combat are inherently deterministic in nature, although considerable effort has been devoted in recent years to introducing stochastic treatments into the theory, for example, by dealing with transition probabilities and “variable” attrition coefficients. We advance the advantageous idea here that the time to kill or time to neutralize key opposing targets is the more logical random variable to be treated on a probabilistic basis, and hence that the fraction of remaining combatants on each side should properly be estimated from the time-to-kill probability distributions sampled—in other words, from principles of the statistical theory of reliability and life testing. The advantages of such treatment include the possibility that the the future course of a battle may be predicted from data on casualties in the early stages of an engagement, and therefore that field commanders will have available information on which to base critical decisions—for example, either to wit...