VERIFICATION ANALYSIS OF ARMSTRONG'S STOCHASTIC SALVO EQUATIONS USING DATA FARMING
Lucas, Thomas W.
Sanchez, Paul J.
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Models such as Hughes’ deterministic salvo equations are used by countries around the world to assist in determining the numbers, capabilities, and employment strategies of their naval warships. Armstrong extended Hughes’ model to create a stochastic salvo model (SSM). Armstrong also evaluated his key assumptions by comparing his closed-form solutions against simulation as a more realistic alternative. This thesis performs a more comprehensive comparison of the SSM versus simulation, utilizing sophisticated design of experiments. Statistical models and case studies are used to identify which combinations of model inputs cause the largest biases (or differences) between the simulation and the SSM. The results show that for independent missiles the SSM closely matches the simulation throughout the region explored. The bias increases when the missiles are correlated or the force levels are large. This is particularly noticeable when estimating the probabilities of zero loss or annihilation. The bias also depends critically on whether the forces are in an overkill, intermediate, or over defense situation. The SSM, our R simulation, and a prototype characteristic function evaluator of the binomial stochastic salvo model are all implemented in a “Shiny” application. This facilitates exploration of the various models within a single user-friendly interface.
Reissued 27 Sep 2018 to reflect correction to equation (1).
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