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Efficient three-level screening designs using weighing matrices. (English) Zbl 1326.62169
Summary: Screening is the first stage of many industrial experiments and is used to determine efficiently and effectively a small number of potential factors among a large number of factors which may affect a particular response. In a recent paper, B. Jones and C. J. Nachtsheim [“A class of three-level designs for definitive screening in the presence of second-order effects”, J. Qual. Technol. 43, No. 1, 1–15 (2011)] have given a class of three-level designs for screening in the presence of second-order effects using a variant of the coordinate exchange algorithm as it was given by R. K. Meyer and C. J. Nachtsheim [Technometrics 37, No. 1, 60–69 (1995; Zbl 0825.62652)]. L. Xiao, D. K. J. Lin and F. Bai [“Constructing definitive screening designs using conference matrices”, J. Qual. Technol. 44, No. 1, 2–8 (2012)] have used conference matrices to construct definitive screening designs with good properties. In this paper, we propose a method for the construction of efficient three-level screening designs based on weighing matrices and their complete foldover. This method can be considered as a generalization of the method proposed by Xiao et al. [loc. cit.]. Many new orthogonal three-level screening designs are constructed and their properties are explored. These designs are highly \(D\)-efficient and provide uncorrelated estimates of main effects that are unbiased by any second-order effect. Our approach is relatively straightforward and no computer search is needed since our designs are constructed using known weighing matrices.

62K05 Optimal statistical designs
62K20 Response surface designs
62K15 Factorial statistical designs
62K25 Robust parameter designs
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