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: In this paper, the concepts of clear effects, alias sets and grid representations are generalized to non-regular two-level designs, and theoretical results for the necessary and sufficient conditions under which there exist nonregular twolevel designs of resolution IV or more containing clear two-factor interactions are proved.
4 citations
TL;DR: An algorithmic framework for generating optimal designs for two-stratum experiments, in which the number of groups and theNumber of observations per group are limited only by upper bounds is proposed and results show that this additional flexibility in the design generation process can significantly improve the quality of the experiments.
4 citations
Cites background from "A graph-aided method for planning t..."
...Sun et al. (1997), Chen et al. (2006), Zhao and Chen (2012) and Wang et al. (2015) also provide grouping schemes for fractional factorial designs, but they focus on maximizing the number of clear effects (Wu and Chen, 1992)....
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...(2015) also provide grouping schemes for fractional factorial designs, but they focus on maximizing the number of clear effects (Wu and Chen, 1992)....
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TL;DR: Based on the effect hierarchy principle, a good design should minimize the confounding among the lower-order effects as discussed by the authors, and it is important to obtain the confounding information of effects of a des...
Abstract: Based on the effect hierarchy principle, a good design should minimize the confounding among the lower-order effects. Thus, it is important to obtain the confounding information of effects of a des...
4 citations
Additional excerpts
...2019 Taylor & Francis Group, LLC (CE) (Wu and Chen 1992), maximum estimation capacity (MEC) (Sun 1993)....
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03 Jan 2012
TL;DR: In this paper, the authors present several criteria for choosing fractional factorial designs, including the popular criterion of minimum aberration, and the issue of optimal blocking of fractional Factorial designs was discussed in Section 13.8.3.4 of HK2.
Abstract: Fractional factorial designs have a long history of successful use in scientific investigations and industrial experiments. This important subject was treated in Chapter 13 of Hinkelmann and Kempthorne (2005), Design and Analysis of Experiments, Volume 2, hereafter referred to as HK2. Several criteria for choosing fractional factorial designs, including the popular criterion of minimum aberration, were briefly presented in Section 13.3.4 of HK2, and the issue of optimal blocking of fractional factorial designs was discussed in Section 13.8.3. These criteria were proposed for choosing designs with better capability of estimating lower-order effects, albeit with different interpretations of such capability. The differences in the interpretations sometimes lead to inconsistences or even contradictions among the different criteria, and one should not expect any criterion to work in all circumstances. In this chapter, we give a
4 citations
TL;DR: For three-level designs, the general minimum lower order confounding (GMC) criterion aims to choose optimal designs by treating aliased component-number pattern (ACNP) as a set.
Abstract: For three-level designs, the general minimum lower order confounding (GMC) criterion aims to choose optimal designs by treating aliased component-number pattern (ACNP) as a set. In this article, we develop some theoretical results of a three-level GMC criterion. The characterizations of three-level GMC designs are studied in terms of complementary sets. All GMC 3n–m designs with N = 3n–m runs and the factor number n = (N – 3r)/2 + i are constructed for r< n – m and i = 0,1,2,3. Furthermore, the confounding information of lower order component effects of GMC 3n–m designs is obtained.
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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