A New Formulation of Lanchester Combat Theory

Frank E. Grubbs and John H. Shuford
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Frank E. Grubbs: U.S. Army Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland
John H. Shuford: The Field Artillery School, Fort Sill, Oklahoma

Operations Research, 1973, vol. 21, issue 4, 926-941

Abstract: 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 withdraw or to augment fighting forces—in order to bring about more desirable future courses of combat for a given mission. Also, commanders may even use analyses suggested herein independently of information on enemy losses to decide whether the course of combat is proceeding satisfactorily or according to plan by comparing data on early casualties observed in an engagement with standards that have been determined from experience or specified in advance. Another advantage of the suggested method is that available Weibull theory leads to placing confidence bounds on the fractions of survivors for any specified mission times. The degree of confidence on final predictions depends, as would be expected, on the number of targets put out of action in an engagement or simulation, the nature of the time to kill distributions encountered or sampled, the degree of accuracy or confidence desired, and the number of runs or the size of the war game. The new formulation is illustrated with a small-scale, but informative, example on a hypothesized engagement between chief battle tanks (CBT's) that fire missiles and R10 tanks with gun armament.

Date: 1973
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