A Novel Framework for Simulation Selection Procedures Based on Multidimensional Drifting Brownian Motions Hitting Ellipsoids

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The research objective of this project is to develop a novel framework for simulation selection procedures using the theory of stochastic processes. The first part is to develop statistical procedures for selection-of-the-best which eliminate inferior systems based on multidimensional drifting Brownian motions hitting ellipsoids. Within this new framework, the conservativeness of statistical procedures due to the Bonferroni inequality can be lessened or completely eliminated. Also to be considered are adjustments in selection procedures to avoid the use of a conservative mean assumption, called slippage configuration, which deteriorates efficiency of many selection procedures when the number of competing alternatives is large. The second part of this research develops feasibility check procedures using a similar approach based on multidimensional drifting Brownian motions. Combining the resulting selection-of-the-best procedures with the new feasibility check procedures will allow solution of constrained selection-of-the-best problems, where the goal is to find the best system under a primary performance measure while also satisfying stochastic constraints on secondary performance measures. The proposed research introduces a new paradigm for designing statistical selection procedures, in which comparisons of systems whose performance must be estimated by experimental sampling or simulation, can be carried out using groups of 3 or more systems at a time rather than using pairwise comparisons. If successful, this research has the potential for dramatically increasing the efficiency of these statistical selection procedures by enabling the rapid screening of inferior systems, which in turn makes them practical for use in large-scale applications such as manufacturing, environmental systems, and health care, examples of settings where simulation is employed due to the complexity of the systems being analyzed.