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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]

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This article presents a method of constructing a rich class of orthogonal designs that include orthogonal Latin hypercubes as special cases. Two prominent features of the method are its simplicity and generality. In addition to orthogonality, the resulting designs enjoy some attractive space-filling properties, making them very suitable for computer experiments. [ABSTRACT FROM PUBLISHER]

We develop a method for construction of arrays which are nearly orthogonal, in the sense that each column is orthogonal to a large proportion of the other columns, and which are convertible to fully orthogonal arrays via a mapping of the symbols in each column to a possibly smaller set of symbols. These arrays can be useful in computer experiments as designs which accommodate a large number of factors and enjoy attractive space-filling properties. Our construction allows both the mappable nearly orthogonal array and the consequent fully orthogonal array to be either symmetric or asymmetric. Resolvable orthogonal arrays play a key role in the construction. [ABSTRACT FROM PUBLISHER]

Abstract: Experiments that study complex real world systems in business, engineering and sciences can be conducted at different levels of accuracy or sophistication. Nested space-filling designs are suitable for such multi-fidelity experiments. In this paper, we propose a systematic method to construct nested space-filling designs for experiments with two levels of accuracy. The method that makes use of nested difference matrices can be easily performed, many nested space-filling designs for experiments with two levels of accuracy can thus be constructed, and the resulting designs achieve stratification in low dimensions. In addition, the proposed method can also be used to obtain sliced space-filling designs for conducting computer experiments with both qualitative and quantitative factors. [Copyright &y& Elsevier]

Abstract: Latin hypercube designs (LHDs) have recently found wide applications in computer experiments. A number of methods have been proposed to construct LHDs with orthogonality among main-effects. When second-order effects are present, it is desirable that an orthogonal LHD satisfies the property that the sum of elementwise products of any three columns (whether distinct or not) is 0. The orthogonal LHDs constructed by , , and all have this property. However, the run size n of any design in the former three references must be a power of two (n=2 c ) or a power of two plus one (n=2 c +1), which is a rather severe restriction. In this paper, we construct orthogonal LHDs with more flexible run sizes which also have the property that the sum of elementwise product of any three columns is 0. Further, we compare the proposed designs with some existing orthogonal LHDs, and prove that any orthogonal LHD with this property, including the proposed orthogonal LHD, is optimal in the sense of having the minimum values of ave(|t|), t max, ave(|q|) and q max. [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]

Computer experiments with qualitative and quantitative factors occur frequently in various applications in science, engineering and business. For choosing input settings of such computer experiments, marginally coupled designs have been proposed in Deng, Hung and Lin (2015) for economic reasons. Although the concept of marginally coupled designs is well understood, the results on design construction are scarce. In addition, the constructed designs may have clustered points for the quantitative factors or cannot accommodate many quantitative factors, especially for two-level qualitative factors. To address this issue, this paper focuses on constructing marginally coupled designs when all qualitative factors have two levels. The proposed construction uses subspace theory in algebra, and the resulting designs can accommodate more quantitative factors while maintaining attractive design properties than the existing approaches. [ABSTRACT FROM AUTHOR]