A Note on Foldover of 2k−pDesigns With Column Permutations

Lin, Dennis K.J.

doi:10.1080/00401706.2015.1044116

Cited by 5 publications

(11 citation statements)

References 17 publications

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“…To remove the complete words in our concatenated designs, we apply sign switches to the generated factors in one or more parent designs. This is because, for a 2 m−p design with possibly permuted factors, sign switches in any set of factors are equivalent to sign switches in a set that only contains generated factors (Li and Lin, 2016) The total number of sets of generated factors for which the signs can be switched in d copies of a 2 m−p design is 2 pd . Evaluating the sign switches in all possible subsets of these factors is computationally infeasible when d > 3 and p > 9.…”

Section: Algorithmic Improvement Of Designsmentioning

confidence: 99%

Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

Vazquez

2018

Technometrics

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Two-level orthogonal arrays of strength 3 permit the study of the main effects and the two-factor interactions of the experimental factors. These arrays are classified into regular and nonregular designs. Good regular designs are available in the literature for large run sizes that are a power of 2. In contrast, good nonregular designs, which have run sizes that are multiples of 8 and are more flexible alternatives to regular designs, are not available for large numbers of runs because their construction is challenging. In this paper, we introduce a collection of strength-3 nonregular designs with large run sizes that, to the best of our knowledge, have not been explored before in the design literature. Using theoretical results and algorithmic approaches, we construct nonregular designs with up to 1280 runs. Our designs fill the gaps between the available strength-3 designs with large run sizes and outperform many comparably-sized benchmark designs in terms of the aliasing among the two-factor interactions. We show the applicability of our collection of strength-3 designs using an infrared sensor experiment. Supplementary materials for this paper are available online.

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Section: Algorithmic Improvement Of Designsmentioning

confidence: 99%

Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

Vazquez

2018

Technometrics

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“…In this section, we first evaluate the performance of our CC/VNS algorithm to generate the best 32-and 64-run concatenated designs with up to 11 factors from strength-3 regular designs with 16 and 32 runs. To this end, we compare our concatenated designs to those obtained by Li and Lin (2016). Next, we assess the performance of our algorithm to generate the best 128-run concatenated designs with up to 30 factors from regular and nonregular designs of strength 3 with 64 runs.…”

Section: Performance Of the Cc/vns Algorithmmentioning

confidence: 99%

“…Their approach involves a complete enumeration of all possible selections of columns in which to switch the signs of the elements. Li and Lin (2016) suggested to also permute the columns of the second parent design before switching the signs in the selected columns.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, this approach also involves an enumeration of column permutations. In any 3 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT case, the end product of the approaches of , , Cheng et al (2008) and Li and Lin (2016) is a concatenation of a parent design with another design that is isomorphic to that parent design (two OAs are said to be isomorphic if one array can be obtained from the other by permuting rows or columns, and switching the signs of the elements in one or more columns). There are two problems with these approaches.…”

Section: Introductionmentioning

confidence: 99%

“…We compare the newly generated designs with the best designs from the literature. In addition to the benchmark designs of Li and Lin (2016), our comparisons involve the regular 64-run designs reported in Chen et al (1993), the 17-factor 64-run design from Cheng et al (2008), the regular 128-run designs reported in Block and Mee (2005) and Xu (2009), the 64-and 128-run designs constructed by Xu and Wong (2007) using quaternary linear codes, and the 64-run designs generated from projections of the folded-over 32-run Hadamard matrix given by the Paley construction. To our knowledge, our study of the projections from this folded-over 32-run Hadamard matrix is new to the literature.…”

Section: Introductionmentioning

confidence: 99%

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Constructing Two-Level Designs by Concatenation of Strength-3 Orthogonal Arrays

2018

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Two-level orthogonal arrays of N runs, k factors and a strength of 3 provide suitable fractional factorial designs in situations where many of the main effects are expected to be active, as well as some two-factor interactions. If they consist of N/2 mirror image pairs, these designs are fold-over designs. They are called even and provide at most N/2 − 1 degrees of freedom to estimate interactions. For k < N/3 factors, there exist strength-3 designs that are not fold-over designs. They are called evenodd designs and they provide many more degrees of freedom to estimate interactions. For N ≤ 48, attractive even-odd designs can be extracted from complete catalogs of strength-3 orthogonal arrays. However, for larger run sizes, no complete catalogs exist. In order to construct even-odd designs with N > 48, we develop an algorithm for an optimal concatenation of strength-3 designs involving N/2 runs. Our approach involves column permutations of one of the concatenated designs, as well as sign switches of the elements of one or more columns of that design. We illustrate the potential of the algorithm by generating two-level even-odd designs with 64 and 128 runs involving up to 33 factors, because this allows a comparison with benchmark designs from the literature. With a few exceptions, our even-odd designs outperform or are competitive with the benchmark designs in terms of the aliasing of two-factor interactions and in terms of the available degrees of freedom to estimate two-factor interactions.

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Classic Regression Metamodels and Their Designs

Kleijnen

2015

International Series in Operations Research &Amp; Management Science

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A Note on Foldover of 2^k−pDesigns With Column Permutations

Cited by 5 publications

References 17 publications

Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

Constructing Two-Level Designs by Concatenation of Strength-3 Orthogonal Arrays

Classic Regression Metamodels and Their Designs

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