A Graph-Aided Method for Planning Two-Level Experiments When Certain Interactions Are Important

Changbao Wu · Youyi Chen

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Optimal Experimental Design Methods Advanced Combinatorial Mathematics Statistical Methods and Applications

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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References

1979Statistics for Experimenters 1991Quality Engineering Using Robust Design 1980Minimum Aberration 2 k-p Designs 1980Minimum Aberration 2k–pDesigns 1991Economical Experimentation Methods for Robust Design

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1992Metamodels for simulation input-output relations 2009A Comprehensive Guide to Factorial Two-Level Experimentation 1995Reliability Improvement with Design of Experiments.2003Optimal Foldover Plans for Two-Level Fractional Factorial Designs 1996$2\sp {n-l}$ designs with weak minimum aberration 1997Optimal Blocking Schemes for 2nand 2n—pDesigns 19982n−m designs with resolution III or IV containing clear two-factor interactions 2005A catalogue of three-level regular fractional factorial designs

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