A system dynamics approach to aircraft survivability-attrition analysis

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Virginia Polytechnic Institute and State University

Mathematical representation of military operations have long fascinated analysts and practitioners. In 1916 English mathematician Frederick W. Lanchester represented the attrition rates of two opposing forces in the form of two differential equations, functions of the size and combat effectiveness of each side. Lanchester's model was an intellectual breakthrough in the analysis of warfare insofar as it provided a deep insight into the possibilities inherent in simple models of combat. Interestingly enough, Lanchester's representation of the problem as a dynamic system is precisely the approach used in the system dynamics methodology employed here. In system dynamics, differential equations are converted to difference equations and there is virtually no limit to the number that can be employed to represent the known and complex details of a system. The attrition model developed here describes the interaction between twelve types of U.S. combat aircraft and twelve types of U.S.S.R. combat aircraft and indicates the winner or the loser at the end of an engagement or a battle during wartime. To guide the peacetime preparations, a generic baseline and modified aircraft are utilized and compared using an adaptation of the attrition model, so as to decide if the proposed modification of U.S. aircraft should be undertaken or not. Two measures of effectiveness are presented to evaluate the overall performance of the modified aircraft compared to the baseline aircraft -- decreased program life cycle cost and increased payload delivered to target per aircraft lost. Scenario analyses are performed to assess the combat aircraft effectiveness under changes to endogenous and exogenous parameters.