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Maximin distance designs and orthogonal designs are two attractive classes of space-filling designs for computer experiments, but their theoretical constructions are challenging, especially the construction of optimal designs in terms of both the maximin distance and orthogonality criteria. This paper presents a systematic method for constructing orthogonal maximin distance designs with flexible numbers of runs and factors. The method is carried out by rotating the subarrays of a saturated two-level regular design in Yates order or its circular shifting version. The principal objective is to construct high-level designs from two-level designs, and the method is effective because the performance of high-level designs is determined by that of two-level designs under both the maximin distance and orthogonality criteria. The proposed method is also generalized by rotating the subarrays of a saturated two-level nonregular design such that the resulting designs have flexible run sizes. Comparison results reveal that the resulting orthogonal designs are well worthy of recommendation under the maximin distance criterion. An illustrative example is provided to show that the proposed designs have a good two-dimensional stratification property. An application is given to present the effectiveness of the proposed designs in building statistical surrogate models. [ABSTRACT FROM AUTHOR]

A growing trend in engineering and science is to use multiple computer codes with different levels of accuracy to study the same complex system. Strategies are needed to combine the simulation results obtained at different levels of accuracy to produce an efficient surrogate model for prediction. In this paper, we propose an integral model to borrow as much information as possible from the low‐accuracy experiment. We ignore the Markov property assumed before and model the high‐accuracy experiment based on an integral form of the low‐accuracy experiment. The proposed model is more general thus better predictions are expected. Two explicit forms of some matrices and vectors used in our predictions are given. The effectiveness of the proposed model is illustrated with several examples. [ABSTRACT FROM AUTHOR]

Strong orthogonal arrays enjoy more attractive space-filling properties than ordinary orthogonal arrays for computer experiments. In this paper, we propose two methods for constructing column-orthogonal nearly strong orthogonal arrays. These designs enjoy column orthogonality, inherit the attractive two-dimensional space-filling property of strong orthogonal arrays, and can accommodate twice or more number of factors than the existing strong orthogonal arrays. In addition, the proposed designs with four levels enjoy an attractive space-filling property under the maximin distance criterion. The construction methods are convenient and flexible, and the resulting designs are useful in computer experiments. • The concept of column-orthogonal nearly strong orthogonal arrays is proposed. • Convenient and flexible construction methods are provided. • New designs have column-orthogonality, space-filling properties and more factors. [ABSTRACT FROM AUTHOR]

In computer experiments, space-filling designs with a sliced structure or nested structure have received much recent interest and been studied separately. However, it is likely that designs with both structures are needed in some situations, but there are no suitable designs so far. In this paper, we construct a special class of nested Latin hypercube designs with sliced structures, in such a design, a small sliced Latin hypercube design is nested within a large one. The construction method is easy to implement and the number of factors is flexible. Numerical simulations show the usefulness of the newly proposed designs. [ABSTRACT FROM PUBLISHER]

Sliced Latin hypercube designs are useful for computer experiments with qualitative and quantitative factors, model calibration, cross validation, multi-level function estimation, stochastic optimization and data pooling. Orthogonality and second-order orthogonality are crucial in identifying important inputs. Besides orthogonality, good space-filling properties are also necessary for Latin hypercube designs. In this paper, a construction method for second-order orthogonal sliced Latin hypercube designs is proposed. The constructed designs are further optimized to achieve better space-filling properties. Furthermore, the method is extended to construct nearly orthogonal sliced Latin hypercube designs. The numbers of slices and columns as well as the levels of the resulting designs are more flexible than those obtained by existing methods. [ABSTRACT FROM AUTHOR]

Abstract: Latin hypercube designs (LHDs) are widely used in computer experiments because of their one-dimensional uniformity and other properties. Recently, a number of methods have been proposed to construct LHDs with properties that all linear effects are mutually orthogonal and orthogonal to all second-order effects, i.e., quadratic effects and bilinear interactions. This paper focuses on the construction of LHDs with the above desirable properties under the Fourier-polynomial model. A convenient and flexible algorithm for constructing such orthogonal LHDs is provided. Most of the resulting designs have different run sizes from that of Butler (2001), and thus are new and very suitable for factor screening and building Fourier-polynomial models in computer experiments as discussed in Butler (2001). [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]

Maximin distance designs and orthogonal designs are extensively applied in computer experiments, but the construction of such designs is challenging, especially under the maximin distance criterion. In this paper, by adding columns to a fold-over optimal maximin L 2 -distance Latin hypercube design (LHD), we construct a class of LHDs, called column expanded LHDs, which are nearly optimal under both the maximin L 2 -distance and orthogonality criteria. The advantage of the proposed method is that the resulting designs have flexible numbers of factors without computer search. Detailed comparisons with existing LHDs show that the constructed LHDs have larger minimum distances between design points and smaller correlation coefficients between distinct columns. • A class of LHDs called column expanded LHDs with flexible numbers of factors are constructed. • The resulting LHDs are nearly maximin L 2 -distance designs. • The resulting designs have small pairwise correlations between columns. [ABSTRACT FROM AUTHOR]

For designs of computer experiments, column-orthogonality and space-filling property are two desirable properties. In this paper, we develop methods for constructing a new class of designs that include orthogonal Latin hypercube designs as special cases. These designs are not only column-orthogonal but also have good space-filling properties in low dimensions. All these appealing properties make them good choices for designing computer experiments. Based on orthogonal arrays, the proposed methods are easy to operate and flexible. Many new orthogonal designs with desirable space-filling properties are constructed and tabulated. Rotation matrices play a key role in the construction. • A new class of space-filling orthogonal designs is proposed. • Convenient and flexible construction methods are provided. • New designs possess attractive two- and three-dimensional space-filling properties. [ABSTRACT FROM AUTHOR]

Maximin distance Latin hypercube designs (LHDs) are extensively applied in computer experiments, but it is challenging to construct such designs. In this paper, based on a 2 2 full factorial design and a series of saturated two-level regular designs, a number of maximin distance LHDs are constructed via the rotation method. Some of the constructed LHDs are exactly optimal and the others are asymptotically optimal under the maximin L 2 -distance criterion. The constructed maximin distance LHDs have two prominent advantages: (i) no computer search is needed; and (ii) they are orthogonal or nearly orthogonal. Detailed comparisons with existing LHDs show that the constructed LHDs have larger minimum distances between design points. • Maximin distance Latin hypercube designs are constructed via the rotation method. • The resulting designs are orthogonal or nearly orthogonal. • The methods are efficient for constructing large designs with no computer search. [ABSTRACT FROM AUTHOR]

Abstract: Computer experiments are becoming increasingly popular in studying complex real world systems. A special class of sliced Latin hypercube design is proposed in this paper. Such designs are particularly suitable for computer experiments with both qualitative and quantitative factors, multi-fidelity computer experiments, cross-validation and data pooling. The resulting sliced Latin hypercube designs possess a desirable sliced structure and have an attractive low-dimensional uniformity. Meanwhile within each slice, it is also a Latin hypercube design with the same low-dimensional uniformity. The new sliced Latin hypercube designs can be constructed via both symmetric and asymmetric orthogonal arrays. The same desirable properties are possessed, although the uniformity may be differed. The construction methods are easy to implement, and unlike the existing methods, the resulting designs are very flexible in run sizes and numbers of factors. A detailed comparison with existing designs is made. [Copyright &y& Elsevier]

Abstract: Sliced Latin hypercube designs are very useful for running a computer model in batches, ensembles of multiple computer models, computer experiments with qualitative and quantitative factors, cross-validation and data pooling. However, the presence of highly correlated columns makes the data analysis intractable. In this paper, a construction method for sliced (nearly) orthogonal Latin hypercube designs is developed. The resulting designs have flexible sizes and most are new. With the orthogonality or near orthogonality being guaranteed, the space-filling property of the resulting designs is also improved. Examples are provided for illustrating the proposed method. [Copyright &y& Elsevier]

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]