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Karunanayaka and Tang (2017) introduced a class of compromise designs for estimating main effects under the baseline parameterization. Their approach is to add some runs to the basic one-factor-at-a-time design, and its implementation requires computer search except for the case of adding one run where a theoretical result is available. The reliance on computer search only allowed them to find the limited results from adding up to four runs to the basic one-factor-at-a-time design. In this paper, we provide a systematic construction of compromise designs, without computer search and without restriction on the run size and the number of factors. Closed-form expressions of the bias and efficiency criteria are obtained for the new designs. Both theoretical and empirical studies show that our designs outperform those of Karunanayaka and Tang (2017) saving small-sized problems. • This paper provides a systematic construction of compromise designs under baseline parameterization. • Closed-form expressions of the bias and efficiency criteria are obtained for the new designs. • The new designs outperform those of Karunanayaka and Tang (2017) saving small-sized problems. [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]

Composite designs are frequently utilized for fitting response surfaces in practice. This paper proposes a new type of composite designs, orthogonal uniform composite designs (OUCDs), which combine orthogonal arrays and uniform designs. Such designs not only inherit the advantages of orthogonal-array composite designs such as high estimation efficiencies and ability for multiple analysis for cross validation, but also have more flexible run sizes than central composite designs and orthogonal-array composite designs. Moreover, OUCDs are more robust than other types of composite designs under certain conditions. Some construction methods for OUCDs under the maximin distance criterion are provided and their properties are also studied. It is shown that many constructed OUCDs are maximin distance designs. • Orthogonal uniform composite designs (OUCDs) have high estimation efficiencies. • OUCDs have more flexible run sizes than many types of composite designs. • OUCDs are robust than other types of composite designs. • Many constructed OUCDs are maximin distance designs. [ABSTRACT FROM AUTHOR]

Fractional factorial split-plot (FFSP) designs are often used when the levels of some factors are difficult to change or control. If not all experimental factors have the same number of levels, mixed-level designs are natural choices. This paper provides the necessary and sufficient conditions for mixed 2- and 2 r -level FFSP designs of resolution III or IV to contain clear main effects or two-factor interaction components. Particularly, the sufficient conditions are proved through constructing the corresponding designs. The new results here are more general and include Zhao and Chen (2012a,b)'s results as special cases for r = 2. • Conditions for some mixed-level FFSP designs with clear effects are provided. • The sufficient conditions are proved through constructing the corresponding designs. • The new results are more general and cover some existing results as special cases. [ABSTRACT FROM AUTHOR]

Abstract: Supersaturated design (SSD) has received much interest because of its potential in factor screening experiments. Inspired by the construction of cyclic orthogonal designs with prime power run numbers in Plackett and Burman (1946), a method for constructing optimal multi-level SSDs with cyclic structure is explored in this paper. Some newly constructed designs are tabulated for practical use. Meanwhile, some of the resulting designs are shown to be also optimal under the criterion. In addition, we show that a sufficient condition for a balanced mixed-level saturated design to be orthogonal is that the weighted coincidence number between any two distinct rows of this design is a constant. An easier proof for the orthogonality of the Plackett and Burman designs with prime power run numbers is also presented. [Copyright &y& Elsevier]

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: Inspired by the ideas of column and row juxtaposition in and level transformation in , this paper presents a new method for constructing optimal supersaturated designs (SSDs). This method provides a convenient way to construct mixed-level designs with relatively large numbers of levels, avoiding the blind search and numerous calculations by computers. The goodness of the resulting SSDs is judged by the ( and ) and J 2 () criteria. Some nice properties of the new designs are also provided. [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]

Abstract: A factorial design can be uniquely determined by an indicator function which is constructed by means of orthogonal contrasts. Since the orthogonal contrasts are not unique, invariant measures are preferred. However, some particular orthogonal contrasts may express more information about designs than the others and be worth our attention. In this paper, a kind of indicator function based on orthogonal complex contrasts is introduced to represent general factorial designs and its significance on projection designs is presented. Based on this function, a generalized resolution and a new aberration criterion are developed to rank combinatorially non-isomorphic designs with prime levels. Some results and comparison are provided by means of examples. [Copyright &y& Elsevier]

Abstract: Supersaturated designs (SSDs) offer a potentially useful way to investigate many factors with only few experiments in the preliminary stages of experimentation. This paper explores how to construct -optimal mixed-level SSDs using k-cyclic generators. The necessary and sufficient conditions for the existence of mixed-level k-circulant SSDs with the equal occurrence property are provided. Properties of the mixed-level k-circulant SSDs are investigated, in particular, the sufficient condition under which the generator vector produces an -optimal SSD is obtained. Moreover, many new -optimal mixed-level SSDs are constructed and listed. The method here generalizes the one proposed by Liu and Dean [2004. -circulant supersaturated designs. Technometrics 46, 32–43] for two-level SSDs and the one due to Georgiou and Koukouvinos [2006. Multi-level k-circulant supersaturated designs. Metrika 64, 209–220] for the multi-level case. [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 Initial screening experiments often leave some problems unresolved, adding follow-up runs is needed to clarify the initial results. In this paper, a technique is developed to add additional experimental runs to an initial supersaturated design. The added runs are generated with respect to the Bayesian D s -optimality criterion and the procedure can incorporate the model information from the initial design. After analysis of the initial experiment with several methods, factors are classified into three groups: primary, secondary, and potential according to the times that they have been identified. The focus is on those secondary factors since they have been identified several times but not so many that experimenters are sure that they are active, the proposed Bayesian D s -optimal augmented design would minimize the error variances of the parameter estimators of secondary factors. In addition, a blocking factor will be involved to describe the mean shift between two stages. Simulation results show that the method performs very well in certain settings. Highlights • Bayesian D s -optimal augmented SSD uses initial-design info to plan follow-up runs. • The factor classification is determined by multiple analysis methods. • The new method considers the shift in average responses between the two experiments. • The Bayesian D s -optimality performs better in certain situations. [ABSTRACT FROM AUTHOR]

Missing observations can hardly be avoided even by a well-planned experiment. Based on the orthogonal-array based composite designs proposed by Xu et al. (2014), new orthogonal-array based composite minimax loss designs are constructed. Comparisons between the proposed designs and other composite designs, including orthogonal-array based composite designs, augmented pairs designs, augmented pairs minimax loss designs, central composite designs, and small composite designs are made in detail, which show that the new composite designs are more robust to one missing design point in terms of the D -efficiency and generalized scaled standard deviation. Moreover, it is demonstrated that the D -efficiency remains unchanged for both level permutation and column permutation in some special cases. [ABSTRACT FROM AUTHOR]

Good lattice point sets have desirable space-filling properties, and many designs with large L 1 -distance can be obtained by the leave-one-out good lattice point method (Zhou and Xu, 2015). However, there are negatively fully correlated columns in such a design. This is undesirable in the modeling of computer experiments. To overcome such a deficiency, we propose a class of designs based on the leave-one-out good lattice point method, whose columns can be divided into two groups, such that any two columns are column-orthogonal when they are from different groups and nearly column-orthogonal when they are in the same group. The new designs can also estimate the linear effects without being correlated with the second-order effects. Moreover, they have good stratification properties and their L 1 -distances are comparable with the corresponding designs in Zhou and Xu (2015). [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]

Supersaturated design (SSD) plays an important role in screening factors. E (f N O D) criterion is one of the most widely used criteria to evaluate multi-level and mixed-level SSDs. This paper provides some methods to construct multi-level E (f N O D) optimal SSDs with general run sizes, which can also be extended to construct mixed-level SSDs. The main idea of these methods is combining two processed generalized Hadamard matrices with the expansive replacement method. These proposed methods are easy to perform. Besides, the non-orthogonality between any two columns of the resulting SSDs is well controlled by that of the source designs. Some illustrative examples are given and several new SSDs are provided in this paper. • Convenient and flexible construction methods are provided. • Many new E (f N O D) optimal supersaturated designs are constructed. • Non-orthogonality of the new designs is well controlled by that of the source designs. [ABSTRACT FROM AUTHOR]

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: A supersaturated design (SSD) is a factorial design in which the degrees of freedom for all its main effects exceed the total number of distinct factorial level-combinations (runs) of the design. Designs with quantitative factors, in which level permutation within one or more factors could result in different geometrical structures, are very different from designs with nominal ones which have been treated as traditional designs. In this paper, a new criterion is proposed for SSDs with quantitative factors. Comparison and analysis for this new criterion are made. It is shown that the proposed criterion has a high efficiency in discriminating geometrically nonisomorphic designs and an advantage in computation. [Copyright &y& Elsevier]

Abstract: Two fractional factorial designs are considered isomorphic if one can be obtained from the other by relabeling the factors, reordering the runs, and/or switching the levels of factors. To identify the isomorphism of two designs is known as an NP hard problem. In this paper, we propose a three-dimensional matrix named the letter interaction pattern matrix (LIPM) to characterize the information contained in the defining contrast subgroup of a regular two-level design. We first show that an LIPM could uniquely determine a design under isomorphism and then propose a set of principles to rearrange an LIPM to a standard form. In this way, we can significantly reduce the computational complexity in isomorphism check, which could only take operations to check two designs in the worst case. We also find a sufficient condition for two designs being isomorphic to each other, which is very simple and easy to use. In the end, we list some designs with the maximum numbers of clear or strongly clear two-factor interactions which were not found before. [Copyright &y& Elsevier]

A supersaturated design (SSD) is a design whose run size is not enough for estimating all the main effects. The goal in conducting such a design is to identify, presumably only a few, relatively dominant active effects with a cost as low as possible. However, data analysis of such designs remains primitive: traditional approaches are not appropriate in such a situation and several methods which were proposed in the literature in recent years are effective when used to analyze two-level SSDs. In this paper, we introduce a variable selection procedure, called the PLSVS method, to screen active effects in mixed-level SSDs based on the variable importance in projection which is an important concept in the partial least-squares regression. Simulation studies show that this procedure is effective. [Copyright &y& Elsevier]

Abstract: Whole-plot (WP) factors and sub-plot (SP) factors play different roles in fractional factorial split-plot (FFSP) designs. In this paper, we consider FFSP designs with resolution III or IV from the viewpoint of clear factorial effects, classify two-factor interactions (2FIs) into three types, and give sufficient and necessary conditions for the existence of FFSP designs containing various clear factorial effects, including two types of main effects and three types of 2FIs. The structures of these designs are also shown and illustrated with examples. [Copyright &y& Elsevier]

Abstract: Blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation. In this article, the clear effect concept is discussed for the blocked fractional factorial designs. First, some theoretical results on the existence of clear main effects and two-factor interactions (2fi''s) in regular designs with resolution III, and IV are obtained, where a design means a design in blocks. Then, the blocked designs containing clear 2fi''s are mainly considered and the upper and lower bounds on the maximum number of clear 2fi''s in designs with resolution III and are derived. The lower bounds are achieved by constructing specific designs. Some tables are also given for comparing the bounds with true values, which show that many designs constructed by our methods have the maximum number of clear 2fi''s. [Copyright &y& Elsevier]