Finding the Active Factors in Fractionated Screening Experiments

George E. P. Box · R. Daniel Meyer

171 citations0/0 files storedJournal of Quality Technology

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Optimal Experimental Design Methods Statistical Methods and Applications Statistical Methods and Bayesian Inference

Abstract

Highly fractionated factorial designs and other orthogonal arrays are powerful tools for identifying important, or active, factors and improving quality. We show, however, that interactions, and important factors involved in those interactions, may go unidentified when conventional methods of analysis are used with these designs. This is particularly true of Plackett-Burman designs where the number of runs is not a power of two. A Bayesian method that allows for the possibility of interactions is developed to compute the marginal posterior probability that a factor is active. The method can be applied to both orthogonal and nonorthogonal designs, as well as other troublesome situations, such as when data are missing, extra data are available, or factor settings for certain runs have deviated from those originally planned. The value of the new technique is demonstrated with three examples in which potential interactions and factors involved in those interactions are uncovered.

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References

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1999Statistics as a Catalyst to Learning by Scientific Method Part II—A Discussion 1996Follow-Up Designs to Resolve Confounding in Multifactor Experiments 2015Multi‐armed bandit experiments in the online service economy 2009Recent developments in nonregular fractional factorial designs 2001Using the Folded-Over 12-Run Plackett—Burman Design to Consider Interactions 2004Optimal Projective Three-Level Designs for Factor Screening and Interaction Detection

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