Fractional Resolution and Minimum Aberration in Blocked 2n—kDesigns

Sitter, R. R.; Chen, Jiahua; Feder, Moshe

doi:10.1080/00401706.1997.10485157

Cited by 9 publications

(3 citation statements)

References 12 publications

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“…In general, if we wish to split the subplot treatments, for each fixed whole‐plot level setting, into 2 r groups, then r splitting factors are required. In this case, the splitting generators, which are similar to blocking generators in blocked FF designs (for example, see Bisgaard (1994) and Sitter et al. (1997)), have an associated defining contrast subgroup.…”

Section: Splitting a 2k1+k2−(0+p2) Fractional Factorial Split Plomentioning

confidence: 99%

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Designing Fractional Factorial Split-Plot Experiments with Few Whole-Plot Factors

Bingham

Schoen²,

Sitter

2004

Journal of the Royal Statistical Society Series C: Applied Statistics

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When it is impractical to perform the experimental runs of a fractional factorial design in a completely random order, restrictions on the randomization can be imposed. The resulting design is said to have a split-plot, or nested, error structure. Similarly to fractional factorials, fractional factorial split-plot designs can be ranked by using the aberration criterion. Techniques that generate the required designs systematically presuppose unreplicated settings of the whole-plot factors. We use a cheese-making experiment to demonstrate the practical relevance of designs with replicated settings of these factors. We create such designs by splitting the whole plots according to one or more subplot effects. We develop a systematic method to generate the required designs and we use the method to create a table of designs that is likely to be useful in practice. Copyright 2004 Royal Statistical Society.

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Section: Splitting a 2k1+k2−(0+p2) Fractional Factorial Split Plomentioning

confidence: 99%

“…We use a similar representation to that used by Bingham and Sitter (1999) (see also Chen et al. (1993) and Sitter et al. (1997)).…”

Section: Splitting a 2k1+k2−(0+p2) Fractional Factorial Split Plomentioning

confidence: 99%

Designing Fractional Factorial Split-Plot Experiments with Few Whole-Plot Factors

Bingham

Schoen²,

Sitter

2004

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…See for example Sitter et al. (1997), Chen and Cheng (1999), Zhang and Park (2000), Cheng and Wu (2002), Xu and Lau (2005), Xu (2006), Xu and Mee (2010) and Zhao et al. (2013).…”

Section: Introductionmentioning

confidence: 99%

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 OMARS designs and definitive screening designs

Ares

Goos

2023

Journal of Quality Technology

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The family of orthogonally minimally aliased response surface or OMARS designs comprises traditional response surface designs, such as central composite designs and Box-Behnken designs, as well as definitive screening designs. Key features of OMARS designs are the facts that they are orthogonal for the main effects and that the main effects are not at all aliased with any two-factor interaction effect or with any quadratic effect. In this article, we present a method to arrange the runs of an OMARS design in blocks of equal size, so that the main effects can be estimated independently from the blocks, and the interaction effects and the quadratic effects are confounded as little as possible with the blocks. We show that our new method for blocking OMARS designs offers much flexibility when it comes to choosing the number of runs, the number of blocks and the block sizes, and that it sometimes yields better blocking arrangements of definitive screening designs than the method of Jones and Nachtsheim (2016).

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Fractional Resolution and Minimum Aberration in Blocked 2^n—kDesigns

Cited by 9 publications

References 12 publications

Designing Fractional Factorial Split-Plot Experiments with Few Whole-Plot Factors

Designing Fractional Factorial Split-Plot Experiments with Few Whole-Plot Factors

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

Blocking OMARS designs and definitive screening designs

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