Equivalent Geometrical Designs with Same Word-Length Pattern  
Author Hsien-Tang Tsai


Co-Author(s) Jen-der Day


Abstract The equivalence (isomorphism) of two given fractional factorial designs has been studied extensively in the literature for more than five decades, in which Hamming distance, J-characteristics and indicator function are often used to provide necessary and sufficient condition for equivalence of two-level fractional factorial designs. In this article, based on the binary column numbers approach, two simple methods of Binary Digit Order Rearrangement (BDOR) and Basic Columns Replacement (BCR) are proposed for obtaining the equivalent design of a given 2k-p geometrical design. In addition, a simple equivalence check algorithm is proposed by combining these two methods. Furthermore, if the proposed methods are used together with joint quaternary design tables, then the users can recognize some special isomorphic designs easily with visually appealing.


Keywords Geometrical design, Equivalent design, Isomorphic design, Wordlength pattern
    Article #:  1911
Proceedings of the 19th ISSAT International Conference on Reliability and Quality in Design
August 5-7, 2013 - Honolulu, Hawaii, U.S.A.