DAE 2024 - Session IV

Session IV (May 15, 3:30pm-5:00pm): Advancements in Screening Design, Nonregular Design, and Space-Filling Design, organized by Ming-Chung Chang

Title: Space-filling Regular Designs under a Minimum Aberration-type Criterion
Speaker: Cheng-Yu Sun, National Tsing Hua University
Abstract: Space-filling designs plays a vital role in computer experiments. Common criteria for selecting such designs are either distance- or discrepancy-based. Recently, Tian and Xu introduced a minimum aberration-type criterion known as the Space-Filling Pattern (SFP). This criterion examines whether a design exhibits stratifications on a series of grids, and can effectively distinguish strong orthogonal arrays of same strengths. Subsequently, Shi and Xu refined the SFP to the stratification pattern (SP). They showed that designs excelling under the SFP can yield better surrogate models than those meeting many other uniformity criteria. In this paper, we propose a novel pattern, referred to as the Sigma-pattern, which is closely related to the SP. We demonstrate that the Sigma-pattern benefits over the SP in certain scenarios, and provide a new justification for both patterns. Then, our focus shits to the construction of space-filling regular designs. We show that the Sigma-pattern of a regular design can be determined by counting different types of words of given lengths. This result allows for a complete search for the most space-filling regular.

Title: On Construction of Nonregular Two-Level Factorial Designs with Maximum Generalized Resolutions
Speaker: Chenlu Shi, Colorado State University
Abstract: The generalized resolution was introduced and justified in Deng and Tang (1999) as a criterion for selecting nonregular factorial designs. Although there have been extensive research activities on other aspects of nonregular designs, developments on the construction of nonregular designs with maximum generalized resolutions pale by comparison. To date, our knowledge of nonregular designs with maximum generalized resolutions is predominantly computational except very few theoretical results. Devoting the whole paper to this topic, we undertake a comprehensive study on the construction of nonregular designs with maximum generalized resolutions. We derive lower bounds on relevant J-characteristics and present construction results. With the assistance of the lower bounds, many of the constructed designs are shown to have maximum generalized resolutions.

Title: Thoughts on supersaturated designs for factor screening experiments
Speaker: John Stufken, George Mason University
Abstract: For a designed experiment with many factors, when observations are expensive, it is common that the number of model effects is much larger than the number of observations. A design for such a problem is known as a supersaturated design. Experiments that use such designs are intended to differentiate between a few factors that can explain most of the differences in a response variable and the factors that are unimportant. Various methods of analysis have been proposed for such experiments, but correctly identifying the few important factors is very challenging because, typically, many models will fit the data approximately equally well. We will discuss some of the challenges and how identifying the important factors may be improved by considering multiple fitted models.