Small Mixed-Level Screening Designs with Orthogonal Quadratic Effects

Nguyen, Nam-Ky; Pham, Tung-Dinh

doi:10.1080/00224065.2016.11918176

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…The sDSDs have, however, also been adapted to deal with two-level categorical factors and with blocking factors. The methods developed by Jones and Nachtsheim (2013) and Nguyen and Pham (2016) to include k two-level categorical factors in a DSD transform the last k columns into two-level columns. Picking other columns than the last k may yield better designs.…”

Section: Discussionmentioning

confidence: 99%

Projections of Definitive Screening Designs by Dropping Columns: Selection and Evaluation

2019

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Definitive screening designs are increasingly used for studying the impact of many quantitative factors on one or more responses in relatively few experimental runs. In practical applications, researchers often require a design for m quantitative factors, construct a definitive screening design for more than m factors and drop the superfluous columns. This is done when the number of runs in the standard m-factor definitive screening design is considered too limited or when no standard definitive screening design exists for m factors. In these cases, it is common practice to arbitrarily drop the last column of the larger definitive screening design. In this paper, we show that certain statistical properties of the resulting experimental design depend on which columns are dropped and that other properties are insensitive to the exact columns dropped. We perform a complete search for the best sets of 1-8 columns to drop from standard definitive screening designs with up to 24 factors. We observed the largest differences in statistical properties when dropping four columns from 8-and 10-factor definitive screening designs. In other cases, the differences are moderate or small, or even nonexistent. Our search for optimal columns to drop necessitated a detailed study of the properties of definitive screening designs. This allows us to present some new analytical and numerical results concerning definitive screening designs.

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Section: Discussionmentioning

confidence: 99%

Projections of Definitive Screening Designs by Dropping Columns: Selection and Evaluation

2019

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“…See (Tutar et al, 2014;Vankanti & Ganta, 2014) for examples on the use of OAs for process improvement. In addition, OAs are used for screening experiments in which the objective is to identify the most important factor effects from a list of many potential ones (Nguyen & Pham, 2016;Xu et al, 2004). Based on the knowledge gained from the screening experiment, the process can be optimised (Xu et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

An Experimental Strategy for Fractionating 33 and 34 Factorial Experiments

Ozoemena¹,

Hackney²,

Birkett³

et al. 2019

IJQR

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In the design of statistical experiments, situations may arise when resource constraints hinder the use of factorial designs for process improvement. This paper explores how 9, 18 and 27-run orthogonal arrays compare against each other and against a proposed experimental plan referred to as a 'Segmented Fractional Plan' when used to fractionate 3 3 and 3 4 factorial experiments. Based on the analysis of 8 responses from 6 factorial experiments, it was observed that to identify the process setting that produces the desired product quality, with a reduced number of experimental runs, the segmented fractional plan can perform as well or better than some orthogonal arrays thus, providing an option for fractionating 3 3 and 3 4 factorial experiments.

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“…The designs are called definitive screening designs. Since their conception, a considerable effort has been invested into the further development of the definitive screening designs; references include Jones and Nachtsheim (2013), Georgiou, Stylianou and Aggarwal (2014), Nguyen and Pham (2016), Jones and Nachtsheim (2017) and Nachtsheim, Shen and Lin (2017). Recent applications have been described by Dougherty et al (2015), Fidaleo et al (2016) and Patil (2017).…”

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confidence: 99%

A classification criterion for definitive screening designs

Schoen

Eendebak²,

Goos³

2019

Ann. Statist.

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A conference design is a rectangular matrix with orthogonal columns, one zero in each column, at most one zero in each row, and −1s and +1s elsewhere. A definitive screening design can be constructed by folding over a conference design and adding a row vector of zeroes. We prove that, for a given even number of rows, there is just one isomorphism class for conference designs with two or three columns. Next, we derive all isomorphism classes for conference designs with four columns. Based on our results, we propose a classification criterion for definitive screening designs based on projections into four factors and illustrate its potential by studying designs with 24 factors. * Supported by the Research Foundation -Flanders FWO MSC 2010 subject classifications: Primary 62K20; secondary 05B20, 94C30

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Small Mixed-Level Screening Designs with Orthogonal Quadratic Effects

Cited by 8 publications

References 13 publications

Projections of Definitive Screening Designs by Dropping Columns: Selection and Evaluation

Projections of Definitive Screening Designs by Dropping Columns: Selection and Evaluation

An Experimental Strategy for Fractionating 33 and 34 Factorial Experiments

A classification criterion for definitive screening designs

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