Stochastic attrition modeling

Abstract

Lanchester’s equations provide a classical way in which to analyze the performance of two combat teams in battle, competing in the case where they are both equipped comparably and where each team’s survivability is a function of the size of the opposing force. This paper introduces a similar approach motivated by analysis of individual’s statistical lifetime distributions. Applying the same principle as in the design of Lanchester’s equations, a stochastic model is suggested, based upon individual’s lifetimes conditional on the size of the opposing force. This novel approach allows variation in individual team members to be included in the analysis, including the case where team members have correlated lifetimes. Hence, it provides a modeling methodology more general than that available through Lanchester’s equations. Based upon fits to real data, a specific model is then applied for individual lifetimes and it is shown how order statistics of the resultant lifetime distributions may be used to analyze combat team survivability.