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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: This work considers the problem of selecting two-level fractional factorial designs that allow joint estimation of all main effects and some specified two-factor interactions (2fi’s) without aliasing from other 2fi”s, and calls a 2 m−p resolution IV design admissible if its graph is not isomorphic to any proper subgraph of the graph of any other 2m−presolution IV design.
Abstract: We consider the problem of selecting two-level fractional factorial designs that allow joint estimation of all main effects and some specified two-factor interactions (2fi’s) without aliasing from other 2fi’s. This problem is to find, among all 2 m−p designs with given m and p, those resolution IV designs whose sets of clear 2fi’s contain the specified 2fi’s as subsets. We use a linear graph to represent the set of clear 2fi’s for a resolution IV design, where each line connecting two vertexes represents a clear 2fi between the factors represented by the two vertexes. We call a 2 m−p resolution IV design admissible if its graph is not isomorphic to any proper subgraph of the graph of any other 2 m−p resolution IV design. We show that all even resolution IV designs are inadmissible. We then use a classical subgraph-isomorphism algorithm to determine all admissible designs of 32, 64, and 128 runs. This leads to a concise catalog of all admissible designs of 32 and 64 runs, and a lengthy but substantially re...

16 citations

Journal ArticleDOI
TL;DR: In this paper, the first term of the wordlengh pattern of regular 2n−m designs has been shown to be the optimal confounding structure for two-level regular designs.

16 citations


Additional excerpts

  • ...Towards this aim, many criteria have been advised in the literature, of which the minimum aberration (MA) criterion proposed by Fries and Hunter (1980) and the clear effects (CE) criterion proposed by Wu and Chen (1992) received most attention in the past two and half decades....

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Journal ArticleDOI
Bong-Jin Yum1, Seongjun Kim, Sun-Keun Seo, Jai-Hyun Byun, Seung-Hoon Lee 
15 Oct 2013
TL;DR: The Taguchi robust design method has been widely used in various fields successfully as mentioned in this paper. But some researchers and practitioners have criticized the method with respect to the way of utilizing orthogonal arrays, the signal-to-noise ratio as a performance measure, data analysis methods, etc.
Abstract: During the past several decades, the Taguchi robust design method has been widely used in various fields successfully. On the other hand, some researchers and practitioners have criticized the method with respect to the way of utilizing orthogonal arrays, the signal-to-noise ratio as a performance measure, data analysis methods, etc., and proposed alternative approaches to robust design. This paper introduces the Taguchi method first, evaluates the validity of the criticisms, and discusses advantages and disadvantages of each alternative. Finally, research issues to be addressed for effective robust design are presented.

15 citations


Additional excerpts

  • ...따라서, CA를 효율적으로 구 성할 필요가 있는 데, 예를 들어 Wu and Chen(1992)은 인자가 모두 2수준이고 추정하고자 하는 교호작용효과들이 알려져 있 을 때, Resolution을 극대화하는 CA의 구성방법을 개발하였다....

    [...]

Journal ArticleDOI
TL;DR: In this article, the mixed-level split-plot designs with four-level factors in both whole-plot and sub-plot sections were studied and conditions under which the designs contain various clear effects and the construction methods of such designs.
Abstract: Mixed-level split-plot designs are commonly used in experiments. This article studies the mixed-level split-plot designs with four-level factors in both whole-plot and sub-plot sections. We give the conditions under which the designs contain various clear effects and the construction methods of such designs.

14 citations


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

  • ...Clear effect criterion (Wu and Chen, 1992) is an important criterion for selecting fractional factorial designs....

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Journal ArticleDOI
TL;DR: Graph-aided methods for accommodating the estimation of interactions in factorial experiments have become popular among industrial users as mentioned in this paper, and notable among them is the method of linear graphs due to Taguchi.
Abstract: Graph-aided methods for accommodating the estimation of interactions in factorial experiments have become popular among industrial users. Notable among them is the method of linear graphs due to Taguchi. Previously, some shortcomings of Taguchi's linear..

14 citations

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