Abstract #300471

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JSM 2003 Abstract #300471
Activity Number: 375
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #300471
Title: Cluster Orthogonal Arrays and Optimal Fractional Factorial Designs
Author(s): Haiyuan Zhu*+ and Sam Hedayat
Companies: Merck & Co., Inc. and University of Illinois, Chicago
Address: 126 E. Lincoln Ave., Rahway, NJ, 07065,
Keywords: orthogonal arrays ; fractional factorial designs ; optimal designs
Abstract:

The family of orthogonal arrays (OAs) enjoys a fascinating mathematical structure. In statistics one of the direct applications of an OA is for forming fractional factorial designs (FFD), perhaps the most useful experimental designs in practice. In constructing optimal FFDs, an important result is that an OA with strength t is a universally optimal resolution t+1 design. If in an experiment factorial effects based on the same number of factors are equally important to be investigated then designs based on OAs are the designs of choice. In some practical situations, however, some of the factorial effects, albeit involving the same number of factors, could be more important than others. In this direction, Hedayat (1990) introduced the concept of OAs of strength t+. Later some other researchers investigated the D-optimality of two-level factorial designs for main effects and selected two-factor interactions. Moving forward in this direction, in this paper, we shall introduce a generalization of OAs, namely Cluster Orthogonal Arrays. Some properties and construction methods will be presented. A connection between cluster orthogonal arrays and the optimal FFDs will also be discussed.

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