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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]

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]

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]

Computer models can describe complicated phenomena encountered in science and engineering fields. To use these models for scientific investigation, however, their generally long running time and mostly deterministic nature require a specially designed experiment. The column-orthogonal design (COD) is a popular choice for computer experiments. Because of the restriction on the orthogonality, however, only little CODs can be constructed. In this article, we propose two algorithms for constructing nearly CODs by rotating orthogonal arrays under two different criteria. Further, some obtained nearly CODs are nearly Latin hypercube designs. Some examples are provided to show the advantages of our algorithms. Some rotation matrices obtained via the algorithms are listed. [ABSTRACT FROM AUTHOR]

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]

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]