Complete enumeration of pure‐level and mixed‐level orthogonal arrays

Schoen, Eric D.; Eendebak, Pieter; Nguyen, Man V.M.

doi:10.1002/jcd.20236

Cited by 107 publications

(104 citation statements)

References 23 publications

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“…We tested the algorithm by comparing our results with those reported in Schoen et al (2010). We also ran other examples.…”

Section: Resultsmentioning

confidence: 99%

“…Orthogonal arrays (OAs) represent an important class of OFFDs, see, for example, Hedayat, Sloane, and Stufken (1999) and Schoen, Eendebak, and Nguyen (2010). Indeed an OA of appropriate strength can be used to solve the wide range of problems related to the study of the size of the main effects and interactions up to a given order of interest.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Minimum-Size Mixed-Level Orthogonal Fractional Factorial Designs Generation: ASAS-Based Algorithm

Fontana¹,

Sampò²

2013

J. Stat. Soft.

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Orthogonal fractional factorial designs (OFFDs) are frequently used in many fields of application, including medicine, engineering and agriculture. In this paper we present a software tool for the generation of minimum size OFFDs. The software, that has been implemented in SAS/IML, puts neither a restriction on the number of levels of each factor nor on the orthogonality constraints. The algorithm is based on the joint use of polynomial counting function and complex coding of levels and follows the approach presented in Fontana (2013).

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“…We tested the algorithm by comparing our results with those reported in Schoen et al (2010). We also ran other examples.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum-Size Mixed-Level Orthogonal Fractional Factorial Designs Generation: ASAS-Based Algorithm

Fontana¹,

Sampò²

2013

J. Stat. Soft.

View full text Add to dashboard Cite

show abstract

“…Note that the catalog is by no means complete; in particular, it is much more difficult to completely enumerate all orthogonal arrays than it is to enumerate all regular orthogonal arrays. Partially complete catalogs of orthogonal arrays are available, e.g., from the website by Eendebak and Schoen (2010) based on the algorithm described in Schoen, Eendebak, and Nguyen (2010). In many cases, the web site provides the best arrays only, or does not provide an array at all (in case of very large numbers of arrays).…”

Section: R> L18mentioning

confidence: 99%

R Package DoE.base for Factorial Experiments

Grömping¹

2018

J. Stat. Soft.

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The R package DoE.base can be used for creating full factorial designs and general factorial experiments based on orthogonal arrays. Besides design creation, some analysis functionality is also available, particularly (augmented) half-normal effects plots. In addition to this specific functionality, the package provides convenience features for analyzing experimental designs and the infrastructure for a suite of further packages on designing and analyzing experiments. This infrastructure is available for use also by further design of experiments packages.

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“…In this paper, we consider the case that all interactions are of equal interest, while the OA need not be embedded in a saturated OA. To generate OAs, we slightly modified the algorithm of Schoen et al (2010) (SEN). The complete source for the system is available on the world wide web (Eendebak, 2015) as well as in the supplementary materials.…”

Section: Candidate Designs For the Motivating Examplementioning

confidence: 99%

Two-Level Designs to Estimate All Main Effects and Two-Factor Interactions

Eendebak

Schoen

2017

Technometrics

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We study the design of two-level experiments with N runs and n factors large enough to estimate the interaction model, which contains all the main effects and all the two-factor interactions. Yet, an effect hierarchy assumption suggests that main effect estimation should be given more prominence than the estimation of two-factor interactions. Orthogonal arrays (OAs) favor main effect estimation. However, complete enumeration becomes infeasible for cases relevant for practitioners. We develop a partial enumeration procedure for these cases and we establish upper bounds on the D-efficiency for the interaction model based on arrays that have not been generated by the partial enumeration. We also propose an optimal design procedure that favors main effect estimation. Designs created with this procedure have smaller D-efficiencies for the interaction model than D-optimal designs, but standard errors for the main effects in this model are improved. Generated OAs for 7-10 factors and 32-72 runs are smaller or have a higher D-efficiency than the smallest OAs from the literature. Designs obtained with the new optimal design procedure or strength-3 OAs (which have main effects that are not correlated with two-factor interactions) are recommended if main effects unbiased by possible two-factor interactions are of primary interest. D-optimal designs are recommended if interactions are of primary interest.

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Complete enumeration of pure‐level and mixed‐level orthogonal arrays

Cited by 107 publications

References 23 publications

Minimum-Size Mixed-Level Orthogonal Fractional Factorial Designs Generation: ASAS-Based Algorithm

Minimum-Size Mixed-Level Orthogonal Fractional Factorial Designs Generation: ASAS-Based Algorithm

R Package DoE.base for Factorial Experiments

Two-Level Designs to Estimate All Main Effects and Two-Factor Interactions

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