Construction of Row–Column Factorial Designs

Godolphin, J. D.

doi:10.1111/rssb.12305

Cited by 11 publications

(14 citation statements)

References 26 publications

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“…A similar result is given in Godolphin (2019) in relation to factorial designs arranged in a rectangular array. Theorem 2 prompts: Corollary 3 If n ≤ 2 q − 1 then all interactions in a blocked 2 n factorial are estimable, provided that X is formed from n distinct members of X q and has rank q, over GF(2).…”

Section: Preliminariessupporting

confidence: 71%

Construction of Blocked Factorial Designs to Estimate Main Effects and Selected Two-Factor Interactions

Godolphin¹

2019

Preprint

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Two-level factorial designs are widely used in industrial experiments. For processes involving n factors, the construction of designs comprising 2 n and 2 n−p factorials, arranged in blocks of size 2 q is investigated. The aim is to estimate all main effects and a selected subset of two-factor interactions. Designs constructed according to minimum aberration criteria are shown to not necessarily be the most appropriate designs in this situation. A design construction approach is proposed which exploits known results on proper vertex colourings in graph theory. Examples are provided to illustrate the results and construction strategies. Particular consideration is given to the special case of designs with blocks of size four and tables of designs are given for this block size.

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Section: Preliminariessupporting

confidence: 71%

Construction of Blocked Factorial Designs to Estimate Main Effects and Selected Two-Factor Interactions

Godolphin¹

2019

Preprint

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“…A result which is similar to Theorem 2 is given in Godolphin (2019) in relation to factorial designs arranged in a rectangular array. Theorem 2 prompts:…”

Section: Blocked Full Factorial Designssupporting

confidence: 66%

Construction of Blocked Factorial Designs to Estimate Main Effects and Selected Two-Factor Interactions

Godolphin

2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Two‐level factorial designs are widely used in industry. For experiments involving n factors, the construction of designs comprising 2n and 2n‐p factorials, arranged in blocks of size 2q is investigated. The aim is to estimate all main effects and a selected subset of two‐factor interactions. Designs constructed according to minimum aberration criteria are shown to not necessarily be the most appropriate designs in this situation. A design construction approach is proposed which exploits known results on proper vertex colourings in graph theory. Examples are provided to illustrate the results and construction strategies. Particular consideration is given to the special case of designs with blocks of size four and tables of designs are given for this block size.

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“…Blocking factors for factorial designs have been well-studied ( [1], [2], [10], [9], [17]). However, as mentioned in [13], having two forms of blocking for a factorial design is less well-studied.…”

Section: Introductionmentioning

confidence: 99%

“…Within experimental design, a row-column design can refer to a variety of combinatorial designs, all with the property of being arranged in a rectangular array, where the rows and columns are typically (but not always) blocking factors. This is sometimes referred to as double confounding [13]. To ensure that certain effects can be estimated without confounding, regularity conditions are imposed.…”

Section: Introductionmentioning

confidence: 99%