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Journal ArticleDOI

A graph-aided method for planning two-level experiments when certain interactions are important

01 May 1992-Technometrics (Taylor & Francis Group)-Vol. 34, Iss: 2, pp 162-175
TL;DR: In this paper, a graph-aided method is proposed to solve the problem of fractional factorial factorial experiment planning, where prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects.
Abstract: In planning a fractional factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects. In this article, we propose a graph-aided method to solve this problem for two-level experiments. First, we choose the defining relations for a 2 n–k design according to a goodness criterion such as the minimum aberration criterion. Then we construct all of the nonisomorphic graphs that represent the solutions to the problem of simultaneous estimation of main effects and two-factor interactions for the given defining relations. In each graph a vertex represents a factor and an edge represents the interaction between the two factors. For the experiment planner, the job is simple: Draw a graph representing the specified interactions and compare it with the list of graphs obtained previously. Our approach is a substantial improvement over Taguchi's linear graphs.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors explore the choice of blocked fractional factorial split-plot designs for use in robust parameter design and provide a ranking scheme for such designs and, using a search algorithm, a catalog of 32-run optimal designs.
Abstract: Fractional factorial experiments are commonly used for robust parameter design and, for ease of use, such experiments are often run as split-plot designs. If the control factors are at the subplot level and the noise factors are at the whole-plot level, this also results in gains in efficiency. If all runs of the fractional factorial split-plot design cannot be run under homogeneous conditions, such designs are frequently blocked. In this paper, we explore the choice of blocked fractional factorial split-plot designs for use in robust parameter design. A ranking scheme for such designs is developed and, using a search algorithm, a catalog of 32-run optimal designs is provided. Two situations are considered, one in which the control factors are at the subplot level and one in which the control factors are at the whole-plot level. An example from the aerospace sector is used to illustrate the concepts.

14 citations

Journal ArticleDOI
TL;DR: In this article, it was proved that some 2-IV m-p designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs.
Abstract: Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2 IV m-p designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some conditions are provided, under which a 2 IV m-p design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak minimum aberration 2 IV m-p designs are provided for illustrations and two nonisomorphic weak minimum aberration 2 IV 13-6 designs are constructed at the end of this paper.

14 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a theory on constructing optimal blocked designs under the blocked general minimum lower order confounding criterion, which is a new criterion for selecting blocked designs, using doubling theory and second order saturated design.
Abstract: Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when the size of the experiment is relatively large. Suitably partitioning inhomogeneous units into homogeneous groups, known as blocks, is a practical design strategy. How to partition the experimental units for a given design is an important issue. The blocked general minimum lower order confounding is a new criterion for selecting blocked designs. With the help of doubling theory and second order saturated design, we present a theory on constructing optimal blocked designs under the blocked general minimum lower order confounding criterion.

14 citations


Cites background from "A graph-aided method for planning t..."

  • ...The second one is based on the clear effects criterion [1,3,15,24]....

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Journal ArticleDOI
TL;DR: In this article, a general decomposition structure of the foldover plan is introduced for general regular s-level fractional factorial designs, where s is any prime or prime power, and the relationships between an initial design and its combined designs are studied.

13 citations


Cites background from "A graph-aided method for planning t..."

  • ...To explain this situation, Wu and Chen (1992) proposed the concept of clear main effect or clear two-factor interaction....

    [...]

01 Jan 2009
TL;DR: In this article, the authors consider two-level orthogonal arrays that allow joint estimation of all main effects and a set of prespecified two-factor interactions, and obtain some theoretical results that provide a simple characterization of when such designs exist, and how to construct them if they do.
Abstract: This paper considers two-level orthogonal arrays that allow joint esti- mation of all main effects and a set of prespecified two-factor interactions. We obtain some theoretical results that provide a simple characterization of when such designs exist, and how to construct them if they do. General as well as concrete applications of the results are discussed.

12 citations


Cites background or methods from "A graph-aided method for planning t..."

  • ...We refer the reader to Wu and Chen (1992), Chen and Hedayat (1998), Wu and Hamada (2000), Wu and Wu (2002) and Tang (2006) for details....

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  • ...Key words and phrases: Clear two-factor interaction, compromise plan, nonregular factorial design, requirement set, robust parameter design....

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  • ...This line of research was further pursued by Franklin and Bailey (1977), Wu and Chen (1992), Dey and Suen (2002), Ke and Tang (2003), and Cheng and Tang (2005)....

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References
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Book
01 Jan 1978

5,151 citations

Book
01 Jan 2015
TL;DR: This book offers a complete blueprint for structuring projects to achieve rapid completion with high engineering productivity during the research and development phase to ensure that high quality products can be made quickly and at the lowest possible cost.
Abstract: From the Publisher: Phadke was trained in robust design techniques by Genichi Taguchi, the mastermind behind Japanese quality manufacturing technologies and the father of Japanese quality control. Taguchi's approach is currently under consideration to be adopted as a student protocol with the US govrnment. The foreword is written by Taguchi. This book offers a complete blueprint for structuring projects to achieve rapid completion with high engineering productivity during the research and development phase to ensure that high quality products can be made quickly and at the lowest possible cost. Some topics covered are: orthogonol arrays, how to construct orthogonal arrays, computer-aided robutst design techniques, dynamic systems design methods, and more.

3,928 citations


"A graph-aided method for planning t..." refers methods in this paper

  • ...For a review on efficient algorithms for testing graph isomorphism, see Read and Corneil (1977) and Hoffman (1982)....

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  • ...For simplicity we do not include in this article the column numbers for the lines, which can be easily read from the interaction tables given by Phadke (1989) and Taguchi (1987)....

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Journal ArticleDOI
TL;DR: The present state of the art of isomorphism testing is surveyed, its relationship to NP-completeness is discussed, and some of the difficulties inherent in this particularly elusive and challenging problem are indicated.
Abstract: The graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP-completeness. No efficient (i.e., polynomial-bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four-color conjecture which prompted Harary to rechristen it the “four-color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP-completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given.

519 citations

Journal ArticleDOI
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.

420 citations

01 Jan 1980
TL;DR: The concept of resolution was introduced by Box and Hunter as discussed by the authors, who defined the resolution of a two-level fractional factorial design as the length of the shortest word in the defining relation.
Abstract: Fractional factorial designs-especially the twolevel designs-are useful in a variety of experimental situations, for example, (i) screening studies in which only a subset of the variables is expected to be important, (ii) research investigations in which certain interactions are expected to be negligible and (iii) experimental programs in which groups of runs are to be performed sequentially, ambiguities being resolved as the investigation evolves (see Box, Hunter and Hunter, 1978). The literature on fractional factorial designs is extensive. For references before 1969, see the comprehensive bibliography of Herzberg and Cox (1969). For more recent references, see Daniel (1976) and Joiner (1975-79). A useful concept associated with 2k-P fractional factorial designs is that of resolution (Box and Hunter, 1961). A design is of resolution R if no cfactor effect is confounded with any other effect containing less than R c factors. For example, a design of resolution III does not confound main effects with one another but does confound main effects with two-factor interactions, and a design of resolution IV does not confound main effects with two-factor interactions but does confound two-factor interactions with one another. The resolution of a two-level fractional factorial design is the length of the shortest word in the defining relation. Usually an experimenter will prefer to use a design which has the highest

354 citations