Hidden projection properties of some nonregular fractional factorial designs and their applications. (English) Zbl 1028.62065

Bulutoglu, Dursun A.; Cheng, Ching-Shui

Ann. Stat. 31, No. 3, 1012-1026 (2003).

Summary: In factor screening, often only a few factors among a large pool of potential factors are active. Under such assumption of effect sparsity, in choosing a design for factor screening, it is important to consider projections of the design onto small subsets of factors. C. S. Cheng [Ann. Stat. 23, 1223-1233 (1995; Zbl 0838.62061); see also Biometrika 85, 491-495 (1998; Zbl 0932.62086)] showed that as long as the run size of a two-level orthogonal array of strength two is not a multiple of 8, its projection onto any four factors allows the estimation of all the main effects and two-factor interactions when the higher-order interactions are negligible. This result applies, for example, to all Plackett-Burman designs whose run sizes are not multiples of 8.
It is shown here that the same hidden projection property also holds for Paley designs [R. E. A. C. Paley, J. Math. Phys., Mass. Inst. Techn. 12, 311-320 (1933; Zbl 0007.10004)] of sizes greater than 8, even when their run sizes are multiples of 8. A key result is that such designs do not have defining words of length three or four. Applications of this result to the construction of \(E(s^2)\)-optimal supersaturated designs are also discussed. In particular, certain designs constructed by using C. F. J. Wu’s method [Biometrika 80, 661-669 (1993)] are shown to be \(E(s^2)\)-optimal. The article concludes with some three-level designs with good projection properties.

MSC:

62K15	Factorial statistical designs
62K05	Optimal statistical designs

Keywords:

Hadamard matrix; orthogonal array; Paley design; Plackett-Burman design; supersaturated design

Citations:

Zbl 0838.62061; Zbl 0932.62086; Zbl 0007.10004

References:

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[23]	BAR HARBOR, MAINE 04609 E-MAIL: [e-mail] DEPARTMENT OF STATISTICS UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA 94720-3860 E-MAIL: [e-mail]