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Recent developments in nonregular fractional factorial designs. (English) Zbl 1300.62056
Summary: Nonregular fractional factorial designs such as Plackett-Burman designs [Biometrika 33, 328–332 (1946; Zbl 0060.31302)] and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. The traditional analysis focuses on main effects only. M. Hamada and C. F. J. Wu [“Analysis of designed experiments with complex aliasing.” J. Quality Technol. 24, 130–137 (1992)] went beyond the traditional approach and proposed an analysis strategy to demonstrate that some interactions could be entertained and estimated beyond a few significant main effects. Their groundbreaking work stimulated much of the recent developments in optimality criteria, construction and analysis of nonregular designs. This paper reviews important developments in nonregular designs, including projection properties, generalized resolution, generalized minimum aberration criteria, optimality results, construction methods and analysis strategies.

MSC:
62K15 Factorial statistical designs
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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