Statistical problems in simulation to be studied include modeling input processes, analyzing output, reducing variance, and designing simulation experiments. Statistical and computational problems involving simulation are motivated by the need to calculate complicated statistical quantities. Most of the problems center around integration, both high dimensional integration and simultaneous integration of thousands of related integrals. The importance of developing fast methods for integrating well behaved, accurately known, functions is highlighted by observing that this is the main obstacle in the way of the creation of a general Bayesian statistical analysis software package. In this project, the simulation approach to numerical integration will be investigated. A taxonomy of manufacturing system models will also be developed. This is a multidiscipliary research project in statistical modeling and stochastic simulation and their use in manufacturing systems design and evaluation. The proposed research program is composed of three distinct, but related, types of projects: statistical problems in simulation, statistical and computational problems involving simulation, and evaluation of statistical and simulation procedures for analyzing manufacturing models. The objective is to develop and refine computational statistics and simulation methodology, with particular emphasis on evaluation and comparison of methods in the context of manufacturing systems. The significance of the research is the development of mathematics and algorithms in computational statistics and stochastic simulation that are relevant to practitioners of statistics and simulation, especially in the manufacturing setting.
