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

本计画的研究目标是利用随机过程理论，发展一个新的模拟选择程序架构。第一部分是开发用于选择最佳的统计程序，该程序基于多维漂移布朗运动击中椭圆体来消除劣质系统。在这个新的框架内，统计程序的保守性，由于邦弗罗尼不等式可以减少或完全消除。还应考虑调整选择程序，以避免使用保守的平均数假设，称为滑移配置，当竞争的备选方案数量很大时，这种假设会降低许多选择程序的效率。本研究的第二部分开发的可行性检查程序，使用类似的方法的基础上，多维漂移布朗运动。结合所产生的选择的最佳程序与新的可行性检查程序将允许解决约束选择的最佳问题，其目标是找到最佳的系统下的主要性能指标，同时也满足随机约束的次要性能指标。 拟议的研究引入了一个新的范式设计统计选择程序，其中的系统，其性能必须通过实验采样或模拟估计的比较，可以进行使用组的3个或更多的系统在同一时间，而不是使用成对比较。如果成功的话，这项研究有可能通过快速筛选劣质系统来显着提高这些统计选择程序的效率，这反过来又使它们实际用于大规模应用，如制造，环境系统和医疗保健，由于系统的复杂性而采用模拟的设置的例子。

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.