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: A more unified approach is taken, developing theoretical results and an efficient relabeling strategy to both construct, and check the isomorphism of, multi-stage factorial designs within a unified framework.
Abstract: Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs has been extensively investigated. Much of the work has been on a case-by-case basis -- addressing completely randomized designs, randomized block designs, split-plot designs, etc. separately. In this paper we take a more unified approach, developing theoretical results and an efficient relabeling strategy to both construct and check the isomorphism of multi-stage factorial designs with randomization restrictions. The examples presented in this paper particularly focus on split-lot designs.
1 citations
Cites background from "A graph-aided method for planning t..."
...These RDCSS-based nonequivalent designs can now be ranked using optimality criteria like maximum resolution (Box and Hunter 1961), minimum abberation (Fries and Hunter 1980), number of clear effects (Wu and Chen 1992), V-Criterion (Bingham et al. 2008), etc....
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...These RDCSS-based nonequivalent designs can now be ranked using optimality criteria like maximum resolution (Box and Hunter 1961), minimum abberation (Fries and Hunter 1980), number of clear effects (Wu and Chen 1992), V-Criterion (Bingham et al....
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25 Jul 2010
TL;DR: In this article, the authors propose a simple method to design minimum aberration experiments, based on orthogonal array, first proposed by Taguchi and Wu, which can be easily adopted by engineers.
Abstract: To achieve the six-sigma quality, the improvement tool of design of experiments can not be ignored. In fact, many six-sigma projects involved the applications of this tool in various companies. To have experimental designs in good quality, we expect to use the best way to set up experiments, so-called minimum aberration experiments. In this article we propose a simple method to design such experiments. The technique used in the method is orthogonal array, first proposed by Taguchi and Wu[1]. This method can be easily adopted by engineers.
1 citations
Cites methods from "A graph-aided method for planning t..."
...For the designs of experiments of size sixteen, we compared them with the minimum aberration designs given in Table 2 of Chen, Sun and Wu [4]....
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...Chen, Sun and Wu [4] used an algorithmic search to find out many minimum aberration designs and some best designs in other criteria, and listed their results in tables....
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...However, the word length patterns of our designs are still on the lists in Chen, Sun and Wu [4]....
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...For the designs of experiments of size thirty-two, we compared them with the minimum aberration designs given in Table 3 of Chen, Sun and Wu [4]....
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...The word length patterns of the resulting designs are exactly the same as those of the minimum aberration designs given in Table 3 of Chen, Sun and Wu [4]....
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TL;DR: In this paper, the authors give a theory on constructing a set of class three clear compromise plans with 5 N ∕ 32 + 3 ≤ n ≤ n ∕ 4 + 1, called partially general minimum lower order confounding (P-GMC) designs.
1 citations
TL;DR: In this paper, a method for the allocation of factors to factor representations is proposed that ensures the optimal estimation of the mean, all main effects and specified 2-factor interactions, in addition to the mean and the main effects are optimally estimable.
1 citations
01 Jan 2018
TL;DR: In this paper, balanced and unbalanced reduced factorial designs for use in optimization of multicomponent behavioral, biobehavioral, and biomedical interventions are discussed, which include a carefully selected subset of the experimental conditions in a corresponding complete factorial.
Abstract: In this chapter, balanced and unbalanced reduced factorial designs for use in optimization of multicomponent behavioral, biobehavioral, and biomedical interventions are discussed. These designs, which include a carefully selected subset of the experimental conditions in a corresponding complete factorial, can be more efficient and economical than complete factorials when implementation of experimental conditions is expensive or logistically challenging. However, there are important trade-offs that the investigator must make in exchange for this efficiency and economy. Reduced factorial designs are not for every situation, but when used appropriately and strategically, they can make excellent use of limited research resources. Readers should be familiar with the material in all previous chapters, particularly Chaps. 3 and 4.
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References
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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