scispace - formally typeset
Search or ask a question
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
More filters
01 Jan 2006

1 citations


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

  • ...[ 3 ] proposed the concepts of clear main effects and clear two-factor interactions (2fis), which are not aliased with any other main effect or two-factor interaction (2fi)....

    [...]

Journal ArticleDOI
TL;DR: The interior principles to calculate the leading elements 1 # C 2 and 2 # C2 in the AENP are shown and their mathematical formulations are obtained for every GMC 2n−m design with N = 2 n−m.
Abstract: The general minimum lower-order confounding (GMC) criterion for two-level design not only reveals the confounding information of factor effects but also provides a good way to select the optimal design, which was proposed by Zhang et al. (2008). The criterion is based on the aliased effect-number pattern (AENP). Therefore, it is very important to study properties of AENP for two-level GMC design. According to the ordering of elements in the AENP, the confounding information between lower-order factor effects is more important than that of higher-order effects. For two-level GMC design, this paper mainly shows the interior principles to calculate the leading elements and in the AENP. Further, their mathematical formulations are obtained for every GMC design with according to two cases: (i) and (ii) .

1 citations


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

  • ...Further, they proved that all the classification patterns conducting the existing criteria, such as maximum resolution (MR) criterion [2], minimum aberration (MA) criterion [3], clear effects (CE) criterion [4], andmaximum estimation capacity (MEC) criterion [5], can be expressed as different functions of the AENP so that it can be a basis to unify these criteria....

    [...]

Journal ArticleDOI
TL;DR: The alias length pattern (ALP) was proposed to characterize the aliasing among two-factor interactions for regular two-level fractional factorial designs of resolution I I I and I V as mentioned in this paper.

1 citations

Dissertation
01 Jan 2013
TL;DR: An A-optimal minimax design criterion for two-level fractional factorial designs is introduced, which can be used to estimate a linear model with main effects and some interactions, and many interesting examples are presented in the thesis.
Abstract: In this thesis we introduce and study an A-optimal minimax design criterion for two-level fractional factorial designs, which can be used to estimate a linear model with main effects and some interactions. The resulting designs are called A-optimal minimax designs, and they are robust against the misspecification of the terms in the linear model. They are also efficient, and often they are the same as A-optimal and D-optimal designs. Various theoretical results about A-optimal minimax designs are derived. A couple of search algorithms including a simulated annealing algorithm are discussed to search for optimal designs, and many interesting examples are presented in the thesis.

1 citations


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

  • ...Consider an example from Wu and Chen (1992) for a 26−2 design with defining relation as I = F1F2F5 = F2F3F4F6 = F1F3F4F5F6....

    [...]

  • ...Those criteria include the maximum resolution criterion in Box and Hunter (1961a, b), the minimum aberration criterion in Fries and Hunter (1980), the clear effects criterion in Wu and Chen (1992), and the maximum estimation capacity criterion in Sun (1993)....

    [...]

  • ...(Wu and Chen, 1992)....

    [...]

References
More filters
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)....

    [...]

  • ...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)....

    [...]

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