Constructing Definitive Screening Designs Using Conference Matrices

Xiao, Lili; Lin, Dennis K.J.; Bai, Fengshan

doi:10.1080/00224065.2012.11917877

Cited by 87 publications

(57 citation statements)

References 4 publications

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“…Finally, the two-variable interactions will be partially aliased with each other. These designs are growing in popularity, with a sizeable literature available on their construction [79,113,82].…”

Section: Nonregular Fractional Factorial Designsmentioning

confidence: 99%

Design of Experiments for Screening

Woods

Lewis

2015

Handbook of Uncertainty Quantification

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The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared. arXiv:1510.05248v1 [stat.ME]

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Section: Nonregular Fractional Factorial Designsmentioning

confidence: 99%

Design of Experiments for Screening

Woods

Lewis

2015

Handbook of Uncertainty Quantification

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“…Assuming that the matrices are skew, the same question has been stated in the problem 104 posted on Cameron's website (see ). This problem arose in the context of experimental designs and it was suggested by Dennis Lin. Concretely, it asks to decide whether or not the following equivalence holds:…”

Section: Introductionmentioning

confidence: 99%

On Skew E–W Matrices

Armario

Frau

2016

J of Combinatorial Designs

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An E–W matrix M is a ( − 1, 1)‐matrix of order 4t+2, where t is a positive integer, satisfying that the absolute value of its determinant attains Ehlich–Wojtas' bound. M is said to be of skew type (or simply skew) if M−I is skew‐symmetric where I is the identity matrix. In this paper, we draw a parallel between skew E–W matrices and skew Hadamard matrices concerning a question about the maximal determinant. As a consequence, a problem posted on Cameron's website [7] has been partially solved. Finally, codes constructed from skew E–W matrices are presented. A necessary and sufficient condition for these codes to be self‐dual is given, and examples are provided for lengths up to 52.

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“…It is known that for N ≡ 2 mod 4, a conference matrix is symmetric. Conference matrices were used for effect screening by Elster and Neumaier (1995) in situations where high-order interactions were thought likely and by Xiao et al (2012) for screening for main effects in the presence of suspected two-factor interactions. The semi-balanced three-level designs of Tsai et al (2000) can also be constructed using conference matrices.…”

Section: Construction Of Q B -Optimal Designsmentioning

confidence: 99%

New families of Q_B-optimal saturated two-level main effects screening designs

Tsai

Gilmour

2016

STAT SINICA

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Abstract:In this paper, we study saturated two-level main effects designs which are commonly used for screening experiments. The QB criterion, which incorporates experimenters' prior beliefs about the probability of factors being active is used to compare designs. We show that under priors with more weight on models of small size, p-efficient designs should be recommended; when models with more parameters are of interest, A-optimal designs would be better. We identify new classes of saturated main effects designs between these two designs under different priors. The way in which the choice of designs depends on experimenters' prior beliefs is demonstrated for the cases when the number of runs N ≡ 2 mod 4. A novel method of construction of QB-optimal designs using conference matrices is introduced. Complete families of optimal designs are given for N = 6, 10, 14, 18, 26, 30.

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Constructing Definitive Screening Designs Using Conference Matrices

Cited by 87 publications

References 4 publications

Design of Experiments for Screening

Design of Experiments for Screening

On Skew E–W Matrices

New families of Q_B-optimal saturated two-level main effects screening designs

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