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Mappable nearly orthogonal arrays were recently proposed as a new class of space-filling designs for computer experiments. Inspired by mappable nearly orthogonal arrays, we propose several new classes of space-filling designs. The corresponding construction methods are provided. The resulting designs are more space-filling than mappable nearly orthogonal arrays while accommodating a large number of factors. In addition to the space-filling properties, the column orthogonality is also desirable for designs of computer experiments. Among the new constructed designs, one class is column-orthogonal, and the other two classes, providing many new column-orthogonal designs, are nearly column-orthogonal in the sense that each column is column-orthogonal to a large proportion of the other columns. The constructed designs are good choices for computer experiments due to their attractive space-filling properties and column orthogonality. The proposed construction methods are flexible in the choices of an orthogonal array and/or a strong orthogonal array and their usefulness is appealing. Many newly constructed space-filling designs are tabulated. The expansive replacement method and the generalized doubling play key roles in the constructions. [ABSTRACT FROM AUTHOR]

In many practical experiments, both the level combinations of factors and the addition orders will affect the responses. However, virtually no construction methods have been provided for such experimental designs. This paper focuses on such experiments, introduces a new type of design called the ordering factorial design, and proposes the nominal main effect component-position model and interaction-main effect component-position model. To obtain efficient fractional designs, we provide some deterministic construction methods. The resulting designs are D -optimal, and the run sizes are much smaller than that of the full designs. Moreover, in some cases, some constructed designs are still D -optimal after reducing the number of components and factors. [ABSTRACT FROM AUTHOR]

For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer grids, including orthogonal Latin hypercube designs (OLHDs) as special cases. In addition to being column-orthogonal, these designs have good space-filling properties in two dimensions. The resulting designs achieve stratifications on s 2 × s or s × s 2 grids, and most column pairs satisfy stratifications on s 2 × s 2 grids. Moreover, many column pairs can achieve stratifications on s 4 × s 2 and s 2 × s 4 grids. Furthermore, the obtained space-filling ODs can have s 6 levels, s 4 levels, and mixed levels, as required for different needs. [ABSTRACT FROM AUTHOR]

Follow-up experimental designs are popularly used in industry. In practice, some important factors may be neglected for various reasons in the first-stage experiment and they need to be added in the next stage. In this paper, we propose a method for augmenting supersaturated designs with newly added factors and augmented levels using the Bayesian D-optimality criterion. In addition, we suggest using the integrated Bayesian D-optimal augmented design to plan the follow-up experiment when the newly added factors have been allowed to vary in an appropriate region. Examples and simulation results show that the augmented designs perform well in improving identified rates of latent factor effects. [ABSTRACT FROM AUTHOR]

Strong orthogonal arrays were recently introduced as a new class of space-filling designs for computer experiments due to their better stratifications than orthogonal arrays. To further improve the space-filling properties in low dimensions while possessing the column orthogonality, we propose column-orthogonal strong orthogonal arrays of strength two star and three. Construction methods and characterizations of such designs are provided. The resulting strong orthogonal arrays, with the numbers of levels being increased, have their space-filling properties in one and two dimensions being strengthened. They can accommodate comparable or even larger numbers of factors than those in the existing literature, enjoy flexible run sizes, and possess the column orthogonality. The construction methods are convenient and flexible, and the resulting designs are good choices for computer experiments. [ABSTRACT FROM AUTHOR]

An attractive type of space-filling design for computer experiments is the class of maximin distance designs. Algorithmic search is commonly used for finding such designs, but this approach becomes ineffective for large problems. Theoretical construction of maximin distance designs is challenging; some results have been obtained recently, often using highly specialized techniques. This article presents an easy-to-use method for constructing maximin distance designs. The method is versatile as it works with any distance measure. The basic idea is to construct large designs from small designs, and the method is effective because the quality of large designs is guaranteed by that of small designs, as evaluated by the maximin distance criterion. [ABSTRACT FROM AUTHOR]

The order-of-addition experiment aims at determining the optimal order of adding components such that the response of interest is optimized. Order of addition has been widely involved in many areas, including bio-chemistry, food science, nutritional science, pharmaceutical science, etc. However, such an important study is rather primitive in statistical literature. In this paper, a thorough study on pair-wise ordering designs for order of addition is provided. The recursive relation between two successive full pair-wise ordering designs is developed. Based on this recursive relation, the full pair-wise ordering design can be obtained without evaluating all the orders of components. The value of the D-efficiency for the full pair-wise ordering model is then derived. It provides a benchmark for choosing the fractional pair-wise ordering designs. To overcome the unaffordability of the full pair-wise ordering design, a new class of minimal-point pair-wise ordering designs is proposed. A job scheduling problem as well as simulation studies are conducted to illustrate the performance of the pair-wise ordering designs for determining the optimal orders. It is shown that the proposed designs are very efficient in determining the optimal order of addition. [ABSTRACT FROM AUTHOR]

The fractional factorial split-plot (FFSP) design is an important experimental design both in theory and in practice. There is extensive literature on the two-level FFSP design and its various variants. However, there is little work on the s-level FFSP design and its variants in the asymmetrical (i.e., mixed-level) case, where s is any prime or prime power. Such designs are commonly used e.g. in agriculture, medicine and chemistry. This paper provides the necessary and sufficient conditions for the existence of resolution III or IV regular s (n 1 + n 2) - (k 1 + k 2) (s r) designs which contain clear main effects or two-factor interaction components. In particular, the sufficient conditions are proved through constructing the corresponding designs, and some examples are provided to illustrate the construction methods. [ABSTRACT FROM AUTHOR]

An efficient variable selection technique for kriging in computer experiments is proposed. Kriging models are popularly used in the analysis of computer experiments. The conventional kriging models, the ordinary kriging, and universal kriging could lead to poor prediction performance because of their prespecified mean functions. Identifying an appropriate mean function for kriging is a critical issue. In this article, we develop a Bayesian variable-selection method for the mean function and the performance of the proposed method can be guaranteed by the convergence property of Gibbs sampler. A real-life application on piston design from the computer experiment literature is used to illustrate its implementation. The usefulness of the proposed method is demonstrated via the practical example and some simulative studies. It is shown that the proposed method compares favorably with the existing methods and performs satisfactorily in terms of several important measurements relevant to variable selection and prediction accuracy. [ABSTRACT FROM AUTHOR]

The uniform design is a kind of important experimental design which has great practical value in production and living. Most existing literatures on this topic focus on the construction of uniform designs on regular regions. However, because of the complexity of practical situations, the irregular design region is more common in real life. In this paper, an algorithm is proposed to the construction of nearly uniform designs on irregular regions. The basic idea is to make use of uniform designs on a larger regular region with the irregular region being a subregion. Some theoretical justifications on the proposed algorithm are provided. Both the comparisons with the existing results and a real-life example show that our proposed algorithm is effective. [ABSTRACT FROM PUBLISHER]

U-type designs and orthogonal Latin hypercube designs (OLHDs) have been used extensively for performing computer experiments. Both have good spaced filling properties in one-dimension. U-type designs may not have low correlations among the main effects, quadratic effects and two-factor interactions. On the other hand, OLHDs are hard to be found due to their large number of levels for each factor. Recently, alternative classes of U-type designs with zero or low correlations among the effects of interest appear in the literature. In this paper, we present new classes of U-type or quantitative $$3$$ -orthogonal designs for computer experiments. The proposed designs are constructed by combining known combinatorial structures and they have their main effects pairwise orthogonal, orthogonal to the mean effect, and orthogonal to both quadratic effects and two-factor interactions. [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]

A supersaturated design (SSD), whose run size is not enough for estimating all the main effects, is commonly used in screening experiments. It offers a potential useful tool to investigate a large number of factors with only a few experimental runs. The associated analysis methods have been proposed by many authors to identify active effects in situations where only one response is considered. However, there are often situations where two or more responses are observed simultaneously in one screening experiment, and the analysis of SSDs with multiple responses is thus needed. In this paper, we propose a two-stage variable selection strategy, called the multivariate partial least squares-stepwise regression (MPLS-SR) method, which uses the multivariate partial least squares regression in conjunction with the stepwise regression procedure to select true active effects in SSDs with multiple responses. Simulation studies show that the MPLS-SR method performs pretty good and is easy to understand and implement. [ABSTRACT FROM AUTHOR]

Various optimal criteria have been proposed to rank asymmetrical fractional factorial designs. Among them, the generalized minimum aberration and the minimum moment aberration criteria are the most popular ones and have received much attention. Recently, Liu et al. (Stat Sin 16:1285-1297, 2006) proposed the minimum χ criterion in terms of level-combinations. In this paper, the equivalency of the generalized minimum aberration and the minimum χ criteria is reported, which not only provides another justification for each other but also develops some theoretical results for designs with generalized minimum aberration and some lower bounds for the generalized wordlength pattern. Besides, an analytic relationship between generalized minimum aberration and minimum moment aberration is obtained for asymmetrical fractional factorial designs. [ABSTRACT FROM AUTHOR]

Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L-( CD) and wrap-around L-discrepancy ( WD) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. [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]

Combinatorial designs have long had substantial application in the statistical design of experiments, and in the theory of error-correcting codes. Applications in experimental and theoretical computer science, communications, cryptography and networking have also emerged in recent years. In this paper, we focus on a new application of combinatorial design theory in experimental design theory. E(fNOD) criterion is used as a measure of non-orthogonality of U-type designs, and a lower bound of E(fNOD) which can serve as a benchmark of design optimality is obtained. A U-type design is E(fNOD)-optimal if its E(fNOD) value achieves the lower bound. In most cases, E(fNOD)-optimal U-type designs are supersaturated. We show that a kind of E(fNOD)-optimal designs are equivalent to uniformly resolvable designs. Based on this equivalence, several new infinite classes for the existence of E(fNOD)-optimal designs are then obtained. [Copyright &y& Elsevier]