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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.

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