Stella Stylianou

A class of composite designs for response surface methodology

A class of efficient and economical response surface designs that can be constructed using known designs is introduced. The proposed class of designs is a modification of the Central Composite Designs, in which the axial points of the traditional central composite design are replaced by some edge points of the hypercube that circumscribes the sphere of zero center and radius a. An algorithm for the construction of these designs is developed and applied. The constructed designs are suitable for sequential experimentation and have higherD-values than those of known composite designs. The properties of the constructed designs are further discussed and evaluated in terms of rotatability, blocking, and D-optimality under the full second-order model.

Efficient three-level screening designs using weighing matrices

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, Jones and Nachtsheim [A class of three-level designs for definitive screening in the presence of second-order effects. J. Qual. Technol. 2011;43:1–15] 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 Meyer and Nachtsheim [The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 1995;37:60–69]. Xiao et al. [Constructing definitive screening designs using conference matrices. J. Qual. Technol. 2012;44:2–8] 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. [Constructing definitive screening designs using conference matrices. J. Qual. Technol. 2012;44:2–8]. 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.

Constructing Definitive Screening Designs Using Cyclic Generators

Jones and Nachtsheim (2011) propose a new class of computer-generated three-level screening designs called definitive screening designs (DSDs). These designs provide estimates of main effects that are unbiased by any second-order effect and require only one more than twice the number of factors. Stylianou (2011) and Xiao et al. (2012) suggest the construction of these designs using conference matrices. The resulting DSD is always global optimum. This method is only applicable when the number of factors is even. This article introduces an algorithm for constructing DSDs for both even and odd numbers of factors using cyclic generators. We show that our algorithm can construct designs that are more efficient than those of Jones and Nachtsheim (2011) and that it can construct much larger designs.

Foldover Conference Designs for Screening Experiments

A conference matrix is a square matrix C with zeros on the diagonal and ±1s off the diagonal, such that C T C = CC T = (n − 1)I, where I is the identity matrix. Conference matrices are an important class of combinatorial designs due to their many applications in several fields of science, including statistical-experimental designs, telecommunications, elliptic geometry, and more. In this article, conference matrices and their full foldover design are combined together to obtain an alternative method for screening active factors in complicated problems. This method provides a model-independent estimate of the set of active factors and also gives a linearity test for the underlying model.

Construction and analysis of edge designs from skew-symmetric supplementary difference sets

ABSTRACT The purpose of screening experiments is to identify the dominant variables from a set of many potentially active variables which may affect some characteristic y. Edge designs were recently introduced in the literature and are constructed by using conferences matrices and were proved to be robust. We introduce a new class of edge designs which are constructed from skew-symmetric supplementary difference sets. These designs are particularly useful since they can be applied for experiments with an even number of factors and they may exist for orders where conference matrices do not exist. Using this methodology, examples of new edge designs for 6, 14, 22, 26, 38, 42, 46, 58, and 62 factors are constructed. Of special interest are the new edge designs for studying 22 and 58 factors because edge designs with these parameters have not been constructed in the literature since conference matrices of the corresponding order do not exist. The suggested new edge designs achieve the same model-robustness as the traditional edge designs. We also suggest the use of a mirror edge method as a test for the linearity of the true underlying model. We give the details of the methodology and provide some illustrating examples for this new approach. We also show that the new designs have good D-efficiencies when applied to first order models.