Experiments in error propagation within hierarchal combat models

Abstract

The Office of the Chief of Naval Operations (OPNAV) uses a hierarchy of simulation models as part of scenario-based planning to help decide which new platforms to procure and how to employ them. Simulation is used at every level of the acquisition process, from platform design to tactics to force structure. In hierarchal combat modeling, the mean output of lower-level, higher-resolution models are used as inputs to higher-level, lower-resolution models. The goal of this process is to inform military commanders how design changes in new platforms will affect tactical performance, and how changes in tactical performance can enhance campaign effectiveness. This thesis uses a hierarchal modeling structure to examine whether including the distributions of mission model inputs instead of just the mean can affect campaign model results. A mission model of a one-on-one submarine battle is developed to determine the mean time to kill (MTTK) for the belligerents. The MTTK is sampled in a variety of ways, including just the mean, and used to calculate the attrition coefficients for a stochastic Lanchester campaign model that contains 18 Blue and 25 Red submarines. The outputs of the campaign models are analyzed statistically. The results indicate that the sampling methodology has a significant impact on the mean probability Blue wins the campaign and the mean amount of losses Blue takes when it wins. In addition, sampling methodology has a significant effect on the standard deviation for the probability Blue wins and the amount of losses Blue expects to take when it wins. These results also have practical significance: estimates of Blue’s average odds of winning range from 0.58 to 0.94, while estimates of average losses range from 4.69 to 8.31. Hierarchal combat models must adopt methods for including the entire distribution of lower-level model outcomes in order to better represent risk.