Advances in Design of Computer Experiments

Open Access
Author:
Quinlan, Kevin Randall
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
November 05, 2018
Committee Members:
  • Dennis Kon-Jin Lin, Dissertation Advisor
  • Dennis Kon-Jin Lin, Committee Chair
  • Dennis Keith Pearl, Committee Member
  • David Hunter, Committee Member
  • Enrique Del Castillo, Outside Member
Keywords:
  • Covering Arrays
  • Bayesian Design
  • Plackett and Burman Designs
  • Experimental Run Order
  • Optimization
Abstract:
A $t$-covering array is a design such that any $t$ factor projection contains all possible factor level combinations. This is useful in software development for detecting if a given setting of the computer code will result in an error or not. Traditional covering arrays may not fit the budget of the experimenter. Thus, we consider one measure of incomplete coverage, and find new results on maximizing the $t$-coverage of a design and call these $(1-\epsilon)$ arrays. Additionally, we introduce an algorithm to construct a $t+q$-covering array from multiple $t$-covering arrays. This is most useful when the potential errors from the software are not deterministic. This is desired over exact replication as the multiple tests can be combined to find a stronger covering array. This new method is advantageous over previous methods which focused on prioritization of testing rather than improving coverage. We also introduce some problems when multiple objective functions are of interest. These problems present new challenges due to the fact that optimization of all criteria at once is most likely impossible. First, we consider the case when there is more than one plausible prior in a Bayesian design context. We study this for the Bayesian $D$-criterion in the logistic regression case, but the general methodology is easily extended to other Bayesian design problems. The weighted priors criterion is shown to give robust results relative to competing design choices. Another multiobjective optimization problem of interest is the Latin Hypercube construction problem. Previously a 50-50 weighting of two criteria and a sequential optimization procedure had been applied. We extend their methodology to a Pareto front approach to find optimal Latin Hypercube Designs. Finally, we consider finding optimal run orders for Plackett and Burman designs. Systematic run orders are necessary when there is a known issue that cannot be controlled as a factor in the experimental design. Rather than using a random run order, it is beneficial to optimize the run order to mitigate outside effects. We find trend robust run orders and minimum cost run orders for the Plackett and Burman design.