1 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
The main topic of this thesis is design and analysis of computer and simulation experiments and is dealt with in six papers and a summary report. Simulation and computer models have in recent years received increasingly more attention due to their increasing complexity and usability. Software packages make the development of rather complicated computer models using predefined building blocks possible. This implies that the range of phenomenas that are analyzed by means of a computer model has expanded significantly. As the complexity grows so does the need for efficient experimental designs and analysis methods, since the complex computer models often are expensive to use in terms of computer time. The choice of performance parameter is an important part of the analysis of computer and simulation models and Paper A introduces a new statistic for waiting times in health care units. The statistic is a measure of the extent of long waiting times, which are known both to be the most bothersome and to have the greatest impact on patient satisfaction. A simulation model for an orthopedic surgical unit at a hospital illustrates the benefits of using the measure. Another important consideration in connection to simulation models is the design of experiments, which is the decision of which of the possible configurations of the simulation model that should be tested. Since the possible configurations are numerous and the time to test a single configuration may take minutes or hours of computer time, the number of configurations that can be tested is limited. Papers B and C introduce a novel experimental plan for simulation models having two types of input factors. The plan differentiates between factors that can be controlled in both the simulation model and the physical system and factors that are only controllable in the simulation model but simply observed in the physical system. Factors that only are controllable in the simulation model are called uncontrollable factors and they correspond to the environmental factors in fluencing the physical system. Applying the experimental framework on the simulation model in Paper A shows that the effects of changes in the uncontrollable factors are better understood with the proposed design compared to the alternative and commonly used methods. In papers D and E a modeling framework for analyzing simulation models with multiple noise sources is presented. It is shown that the sources of variation of the simulation model can be divided in two components corresponding to changes in the environmental factors (the uncontrollable factor settings) and to random variation. Moreover, the structure of the environmental effects can be estimated, which can be used to put the system in a more robust operating mode. The interpolation technique called Kriging is the topic of Paper F, which is a widely applied technique for building so called models-for-the-model (metamodels). We propose a method that handles both qualitative and quantitative factors, which is not covered by the standard model. Fitting the final Kriging model is done in two stages each based on fitting regular Kriging models. It is shown that this method works well on a realistic example such as a simulation model for a surgical unit.