DAE 2024 - Session III

Session III (May 15, 1:00pm-2:30pm): Factorial/Multi-level Design, organized by Hongquan Xu

Title: Models for Order-of-addition Screening Experiments
Speaker: Jing-Wen Huang, National Tsing Hua University, Taiwan
Abstract: In many physical and engineering experiments, the order in which a process is executed or components are added can have a marked impact on the response. Due to constraints on resources or feasibility, there are situations where only a subset of the components can be administered in practice and the experimenter encounters a complicated task with the selection of components and its corresponding best order. We present a series of models for such order-of-addition screening experiments and study their properties. We develop theoretical results on the corresponding optimal designs and illustrate these models on job scheduling problems with job rejection penalties.

Title: Construction of Orthogonal-MaxPro Latin Hypercube Designs
Speaker: Qian Xiao, University of Georgia
Abstract: Orthogonal Latin hypercube designs (LHDs) and maximum projection (MaxPro) LHDs are widely used in computer experiments. They are efficient for estimating the trend part and the Gaussian process part of the universal Kriging (i.e., the Gaussian process) model, respectively, especially when only some of the factors are active. Yet, the orthogonality and the MaxPro criteria often do not agree with each other. In this work, we propose a new class of optimal designs, called orthogonal-MaxPro LHDs, optimizing a well-defined multi-objective criterion combining the correlation and the MaxPro metrics. An efficient parallel algorithm via level permutations and expansions is developed, whose efficiency is guaranteed by theories. Numerical results are presented to show that the construction is fast and the obtained designs are attractive, especially for large computer experiments.

Title: Small Mixed-Level Screening Designs
Speaker: Dennis K.J. Lin, Purdue University
Abstract: Screening is an important step of scientific research. It aims to identify a few active factors, among many potential factors. While two-level screening design is well known, the mixed-level screening designs remain primitive. In this talk, two classes of mixed-level screening designs will be discussed. It is shown that the proposed mixed-level designs have most desirable design properties (such as D- and A-efficiencies) and can be straightforwardly constructed without any computing power. Furthermore, when orthogonality is required, a new class of mixed-level orthogonal screening designs with small run sizes will be introduced. These designs are mainly based upon Conference Matrices. It is noticed that different conference matrices may result in different design properties for the constructed designs. Some remarks on this direction will be discussed at the end.