Algorithmic Construction of Efficient Fractional Factorial Designs With Large Run Sizes

• Published in: Technometrics Vol. 51; no. 3; pp. 262 - 277
• Main Author: Xu, Hongquan
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.08.2009; The American Society for Quality and The American Statistical Association; American Society for Quality and the American Statistical Association; American Society for Quality
• Subjects: Algorithms; Applied sciences; Binary codes; Coding theory; Coding, codes; Construction; Design; Design efficiency; Design engineering; Design evaluation; Exact sciences and technology; Experimental design; Factorial design; Factorials; Fractional factorial design; Graphic design; Information, signal and communications theory; Isomorphism; Linear code; MacWilliams identity; Mathematics; Minimum aberration; Probability and statistics; R&D; Research & development; Resolution; Sciences and techniques of general use; Signal and communications theory; Statistics; Telecommunications and information theory; Linear code; Experimental design; MacWilliams identity; Algorithmics; Isomorphism; Factorial design; Fractional factorial design; Catalogs; Minimum aberration; Resolution
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/tech.2009.07120

Fractional factorial (FF) designs are widely used in practice and typically are chosen according to the minimum aberration criterion. A sequential algorithm is developed for constructing efficient FF designs. A construction procedure is proposed that allows a design to be constructed only from its minimum aberration projection in the sequential buildup process. To efficiently identify nonisomorphic designs, designs are categorized according to moment projection pattern. A fast isomorphism checking procedure is developed by matching the factors using their delete-one-factor projections. This algorithm is used to completely enumerate all 128-run designs of resolution 4, all 256-run designs of resolution 4 up to 17 factors, all 512-run designs of resolution 5, all 1024-run designs of resolution 6, and all 2048- and 4,096-run designs of resolution 7. A method is proposed for constructing minimum aberration (MA) designs using only a partial catalog of some good designs. Three approaches to constructing good designs with a large number of factors are suggested. Efficient designs, often with MA, are tabulated up to 40, 80, 160, 45, 47, and 65 factors for 128, 256, 512, 1024, 2048, and 4,096 runs, respectively.