A graph-aided method for planning two-level experiments when certain interactions are important
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.
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TL;DR: This paper presents graphical methods for deciding on experiment goals, selecting and identifying variables, and specifying a model, which are often overlooked in the literature.
Abstract: This paper presents graphical methods for deciding on experiment goals, selecting and identifying variables, and specifying a model. These steps are often overlooked in the literature, where the appropriate variables and model are assumed to be given. T..
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TL;DR: In this article, a set of run conditions for factorial and fractional factorial designs is presented, and a design-plots for viewing the set of conditions for experiment designs is developed.
Abstract: This chapter develops design-plots for viewing the set of run conditions for experiment designs. The emphasis is on factorial and fractional factorial designs but mixture designs nested designs and irregular designs are also presented. The fundamental concept for designs with more than two factors is to place points on a regular grid. By drawing the grid lines in a hierarchical way it is possible to view designs with as many as ten factors. These representations are not projections since all of the factor values for a run can be determined from the location of the corresponding point on the design-plot.
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TL;DR: In this article, the sufficient and necessary conditions for a FFSP design with resolution III or IV to have various clear factorial effects, including two types of main effects and three types of two-factor interaction components, were investigated.
Abstract: Mixed-level designs are widely used in the practical experiments. When the levels of some factors are difficult to be changed or controlled, fractional factorial split-plot (FFSP) designs are often used. This paper investigates the sufficient and necessary conditions for a \({2^{(n_{1}+n_{2})-(k_1+k_2)}4_s^{1}}\) FFSP design with resolution III or IV to have various clear factorial effects, including two types of main effects and three types of two-factor interaction components. The structures of such designs are shown and illustrated with examples.
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Cites background or methods from "A graph-aided method for planning t..."
...Wu and Chen (1992) mentioned an example in a circuit-pack assembly process....
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...It is suitable to carry out the experiment using a mixed-level split-plot design with clear two-factor interactions if there are both two-level and four-level factors in the example (see Wu and Chen 1992 for details)....
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...We refer to Wu and Chen (1992) for some examples....
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...Clear effects (Wu and Chen 1992) is a popular optimality criterion for selecting designs....
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TL;DR: In this article, the authors extend the general minimum lower-order confounding (GMC) criterion to the case of three-level designs and introduce an aliased component number pattern (ACNP) and a threelevel GMC criterion via the consideration of component effects, and obtain some results on the new criterion.
Abstract: In this paper, we extend the general minimum lower-order confounding (GMC) criterion to the case of three-level designs. First, we review the relationship between GMC and other criteria. Then we introduce an aliased component-number pattern (ACNP) and a three-level GMC criterion via the consideration of component effects, and obtain some results on the new criterion. All the 27-run GMC designs, 81-run GMC designs with factor numbers and 243-run GMC designs with resolution or higher are tabulated. The Canadian Journal of Statistics 41: 192–210; 2013 © 2012 Statistical Society of Canada
Dans cet article, nous generalisons le critere de l'amalgame general minimal d'ordre inferieur (GMC) aux plans d'experience a trois niveaux. Dans un premier temps, nous passons en revue les relations entre le GMC et les autres criteres. Par la suite, nous presentons une representation numerique du nombre de composantes de repliement (ACNP) et un critere GMC a trois niveaux en considerant l'effet des composantes. Nous presentons aussi quelques resultats sur ce nouveau critere. Nous avons catalogue tous les devis GMC a 27 iterations et a 81 iterations ayant un nombre de facteurs egaux a et les devis GMC a 243 iterations ayant une resolution ou superieure. La revue canadienne de statistique 41: 192–210; 2013 © 2012 Societe statistique du Canada
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TL;DR: In this article, the minimum aberration of type WP (WP-MA) was proposed as an optimal criterion for fractional factorial split-plot (FFSP) design under the circumstances that the experimenter has some prior information about the significance of the WP factors.
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Book•
01 Jan 2015TL;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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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
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