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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.

AbstractIn 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.

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Citations
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Journal ArticleDOI
TL;DR: A group of practitioners and researchers discuss the role of parameter design and Taguchi's methodology for implementing it and the importance of parameter-design principles with well-established statistical techniques.
Abstract: It is more than a decade since Genichi Taguchi's ideas on quality improvement were inrroduced in the United States. His parameter-design approach for reducing variation in products and processes has generated a great deal of interest among both quality practitioners and statisticians. The statistical techniques used by Taguchi to implement parameter design have been the subject of much debate, however, and there has been considerable research aimed at integrating the parameter-design principles with well-established statistical techniques. On the other hand, Taguchi and his colleagues feel that these research efforts by statisticians are misguided and reflect a lack of understanding of the engineering principles underlying Taguchi's methodology. This panel discussion provides a forum for a technical discussion of these diverse views. A group of practitioners and researchers discuss the role of parameter design and Taguchi's methodology for implementing it. The topics covered include the importance of vari...

633 citations


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

  • ...One possible strategy, adopted by Wu and Chen (1992), is to search for designs that optimize resolution and aberration subject to the constraint that they must satisfy the requirement set....

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  • ...These problems are resolved in an improved version proposed by Wu and Chen (1992)....

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  • ...As shown by Wu and Chen (1992)) for larger problems Taguchi’s method is deficient....

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  • ...For small to medium problems, the method of linear graphs and the modification due to Wu and Chen (1992) save experimenters from doing the tedious work of finding a feasible solution....

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  • ...Interaction graphs (Kacker and Tsui 1990), improved linear graphs (Wu and Chen 1992)) and confounding tables (Tsui 1988) are effective for this purpose....

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Journal ArticleDOI
TL;DR: In this paper, the algebraic structure of fractional factorial (FF) designs with minimum aberration is explored and an algorithm for constructing complete sets of FF designs is proposed.
Abstract: Summary Fractional factorial (FF) designs with minimum aberration are often regarded as the best designs and are commonly used in practice. There are, however, situations in which other designs can meet practical needs better. A catalogue of designs would make it easy to search for 'best' designs according to various criteria. By exploring the algebraic structure of the FF designs, we propose an algorithm for constructing complete sets of FF designs. A collection of FF designs with 16, 27, 32 and 64 runs is given.

252 citations

Journal ArticleDOI
TL;DR: In this article, the authors summarized the statistical methods for planning and analyzing robust design experiments originally proposed by Taguchi; then reviewed newly developed statistical methods and identified areas and problems where more researches are needed.
Abstract: Robust Design is an important method for improving product quality, manufacturability, and reliability at low cost. Taguchi's introduction of this method in 1980 to several major American industries resulted in significant quality improvement in product and manufacturing process design. While the robust design objective of making product performance insensitive to hard-to-control noise was recognized to be very important, many of the statistical methods proposed by Taguchi, such as the use of signal-to-noise ratios, orthogonal arrays, linear graphs, and accumulation analysis, have room for improvement. To popularize me use of robust design among engineers, it is essential to develop more effective, statistically efficient, and user-friendly tech niques and tools. This paper first summarizes the statistical methods for planning and analyzing robust design experiments originally proposed by Taguchi; then reviews newly developed statistical methods and identifies areas and problems where more resear...

250 citations

Proceedings ArticleDOI
01 Dec 1992
TL;DR: A state of the art review of recent developments in metarnodels, which discusses seven alternative modeling strategies that are active topics in the current literature.
Abstract: The simulation community has used metarnodels to study the behavior of computer simulations for over twenty-five years. The most popular teebniques have been based on parametric polynomial response surface approximations. In this state of the art review, we present recent developments in this area. We also discuss seven alternative modeling strategies that are active topics in the current literature.

180 citations


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

  • ...Phadke 1989, Kacker and Tsui 1990, and Wu and Chen 1992 for details)....

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  • ...…for choosing appropriate fractional factorial experiment designs is not generally available (but see Shoemaker and Tsui s concluding remarks in Nair, et al. 1992), graphical methods ease this task (see Taguchi 1959 (960), Phadke 1989, Kacker and Tsui 1990, and Wu and Chen 1992 for details)....

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Book
01 Jul 1993
TL;DR: This work demonstrates how to use design of experiments for concurrent product design, process development and reliability engineering.
Abstract: Shows how to set up and operate a practical reliability programme using the design of experiments to provide the required information. Emphasizing real solutions, this work demonstrates how to use design of experiments for concurrent product design, process development and reliability engineering.

138 citations


References
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Book
01 Jan 1978

5,099 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.

3,862 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.

501 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.

415 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

338 citations