Classification of Three-word Indicator Functions of Two-level Factorial Designs

Abstract

Fractional factorial design, Indicator function, Word, Non-regular design, Foldover design,

Advances in Robust Parameter Design: From Taguchi's Inner‐Outer Arrays to Combined Arrays

“…Cheng and Ye [12] studied three-level orthogonal arrays under geometric isomorphism, while Tsai et al [40] and Xu et al [46] offered optimal three-level orthogonal arrays for certain experimental situations. Moreover, Lam and Tonchev [22,23] found 68 nonisomorphic OA (27,13,3, 2)'s. Recently, Evangelaras et al [17,18] enumerated and classified all orthogonal arrays with q three-level columns and n = 18 and 27 runs.…”

“…Yang [3] presented properties of indicator functions, while Loeppky et al [26] used indicator functions to select optimal nonregular experimental plans for the robust parameter problem.…”

Forms of four-word indicator functions with implications to two-level factorial designs

“…. , m. By Remark 1 in Balakrishnan and Yang (2006a), the signs of any two words can be all the possible combined signs, as follows:…”

“…Note that if we know the indicator function of an unreplicated design, then the indicator function of the complete replicates of the design can be obtained by multiplying the number of the replicates. Balakrishnan and Yang (2006a) considered indicator functions of unreplicated designs with one to three words. In this paper, we study the forms of the indicator functions with four words.…”

Some lower bounds of centered $$L_2$$ L 2 -discrepancy of $$2^{s-k}$$ 2 s - k designs and their complementary designs

“…Cheng and Ye (2004) and Pistone and Rogantin (2008) studied the representation of an asymmetrical fractional factorial design by its indicator polynomial function, respectively. Balakrishnan and Yang (2006a) and Balakrishnan and Yang (2011) classified a kind of two-level factorial designs with three-or four-word indicator functions, respectively. Balakrishnan and Yang (2006b) studied the connection between general two-level factorial designs of generalized resolutions by using indicator function.…”