Essays on survivability in stochastic duels

Today, the U.S. Army conducts more operations with fewer soldiers than ever before. Inherent in these operations is the possibility of casualties among our soldiers: consequently, we motivate this research with a desire to better equip our soldiers to survive these operations. We first present a paradigm to describe combat survivability. Then, we offer analysis to suggest that one can gain insight into the survivability of the combat vehicles in a force by studying such a vehicle in a one-on-one duel between that combatant and an adversary. Next, we present a model for the survivability of a given combatant; however, we suggest that while this model is mathematically valid, it is not accessible by the journeymen engineers who design combat vehicles for the U.S. Army.; To improve the accessibility of this model, we set the implementation of this model in renewal theory as our first research goal. Because of this approach, one can easily visualize a combatant's engagement process. Thus, survivability engineers can take measures to mitigate the risk of damage posed by an adversary's weapon and assess their efforts on an engineering level using a statistically valid measure that describes platform survivability. Having established a basic renewal formulation for a combatant, we incorporate the process of target detection by modeling that combatant using a delayed renewal equation. We complete our efforts to improve accessibility by coupling the renewal formulation of a combatant to our paradigm of survivability and by illustrating how one can incorporate survivability measures into the engagement process.; We set our next goal as the construction and validation of a computer simulation of our methods. Using the MATLAB programming language, we construct two different computer simulations to model a combatant's firing process. We assess each model by comparing its outputs to analytical results from the literature. Finally, we propose a test case to illustrate the applicability of this research. We first obtain an analytical solution, and then we validate this result using our simulations. Our analysis indicates that this approach can benefit those who design combat vehicles for the U.S. Army.