New Developments in Statistical Optimal Designs for Physical and Computer Experiments

Statistical design of experiments allows for multiple factors influencing a process to be systematically manipulated in an experiment, and their effects on the output of the process to be studied via statistical modeling and analysis. Classical designs offer general nice performance but have limited applications due to restricted design size, region, and randomization structure. Computer generated optimal designs become more popular in recent decades due to the rapid growth in computing power. Most existing work in optimal design of experiments involves designing experiments with optimal performance on a single chosen objective or a single response. However, with the increasing limitation in resources and emergence of complex engineering problems, more and more experiments aim to simultaneously achieve multiple objectives or study multiple responses. Recent developments have made enhancements on methodologies for selecting optimal designs based on multiple criteria for a single response from a physical experiment. However, there has been limited work on constructing optimal designs for a physical experiment with multiple responses. In the area of design of computer experiments, despite space-filling designs have been most popular due to their flexibility on model choices, existing space-filling designs are mainly built for optimizing a single criterion, which is often associated with worse performance on other characteristics. In addition, modern design of experiment techniques which provide powerful tools for efficient data collection and inferential analysis have not been broadly used in the field of reliability analysis. This dissertation adds to the growing research in optimal design of experiments in three different areas: 1. It develops new cost-efficient optimal designs for obtaining precise estimation of multiple responses from a single experiment by leveraging prior information from earlier screening experiment; 2. It proposes new Latin hypercube designs for computer experiments based on balancing multiple space-filling characteristics; and 3. It utilizes Bayesian optimal design technique for selecting optimal test plans for accelerated degradation tests with two or more accelerating factors and more general degradation path models