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Strong orthogonal arrays are suitable designs for computer experiments because of stratification in low‐dimensional projections. However, strong orthogonal arrays may be very expensive for a moderate number of factors. In this article, we develop a method for constructing space‐filling designs with more economical run sizes. These designs are not only column‐orthogonal but also enjoy a large proportion of low‐dimensional stratification properties that strong orthogonal arrays ought to have. Moreover, a class of proposed designs can be 3‐orthogonal. In addition, some theoretical results on regular fractional factorial designs are obtained as a by‐product. [ABSTRACT FROM AUTHOR]

A supersaturated design (SSD) is a factorial design whose run size is not enough for estimating all the main effects. Such designs have received much recent interest because of their potential in factor screening experiments. This paper first shows that the design obtained by the Kronecker sum of a balanced design and a generalized Hadamard matrix (i.e., a matrix with both itself and its transpose being difference matrices) has some nice properties. Based on these findings, some new methods for constructing E (f NOD) -optimal SSDs via generalized Hadamard matrices are developed. Meanwhile, the non-orthogonality of the proposed designs is well controlled by the source designs. In addition, some generalized Hadamard matrices with nice properties are constructed for obtaining E (f NOD) -optimal SSDs. The proposed methods are easy to implement and many new SSDs can then be constructed. [ABSTRACT FROM AUTHOR]

An order-of-addition experiment is a kind of experiment in which the response is affected by the addition order of materials or components. In many situations, performing the full design with all possible permutations of components is unaffordable, especially when the number of components is larger than four. We introduce a component-position model for analyzing data from such experiments and study associated problems. We further propose a new type of design, called component orthogonal array, as a fraction of the full design for order-of-addition experiments. It is shown that component orthogonal arrays have the same D-efficiency as the full design under our proposed model. Component orthogonal arrays also perform well under the existing pairwise ordering model. Two drug combination experiments are used to show the effectiveness of the proposed model and designs. Supplementary materials for this paper are available online. [ABSTRACT FROM AUTHOR]

Abstract: Factorial designs are arguably the most widely used designs in scientific investigations. Generalized minimum aberration (GMA) and uniformity are two important criteria for evaluating both regular and non-regular designs. The generation of GMA designs is a non-trivial problem due to the sequential optimization nature of the criterion. Based on an analytical expression between the generalized wordlength pattern and a uniformity measure, this paper converts the generation of GMA designs to a constrained optimization problem, and provides effective algorithms for solving this particular problem. Moreover, many new designs with GMA or near-GMA are reported, which are also (nearly) optimal under the uniformity measure. [Copyright &y& Elsevier]

Computer experiments are widely used in modern science and industrial applications that require space-filling designs. Uniform projection designs (UPDs) have recently been proposed to address designs' space-filling properties for low-dimensional projections. UPDs are desirable for experiments in which only portions of factors are active. The construction of UPDs with flexible sizes is challenging, especially for large ones. In this paper, we systematically study the construction methods of UPDs via level permutation and/or level expansion. For each approach, we establish theoretical results connecting the uniform projection properties of the generated designs with the properties of the corresponding initial designs. Based on the established theoretical results, efficient algorithms are developed to construct UPDs with flexible sizes, which leads to many practically useful designs. [ABSTRACT FROM AUTHOR]

Modern experiments typically involve a very large number of variables. Screening designs allow experimenters to identify active factors in a minimum number of trials. To save costs, only low-level factorial designs are considered for screening experiments, especially two- and three-level designs. In this article, we provide a systematic method to construct screening designs that contain both two- and three-level factors based on Hadamard matrices with the fold-over structure. The proposed designs have good performance in terms of D-optimal and A-optimal criteria, and the estimates of the main effects are unbiased by the second-order effects, making them very suitable for screening experiments. Besides, some theoretical results on D- and A-optimality are obtained as a by-product. • The new method is easy to implement, utilizing Hadamard matrices and a fold-over structure. • The proposed designs have good performance in terms of D-optimal and A-optimal criteria. • The resulting designs ensure that the estimates of the main effects are unbiased for second-order effects. [ABSTRACT FROM AUTHOR]