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Experiments using designs with complex aliasing patterns are often performed-for example, twolevel nongeometric Plackett-Burman designs, multilevel and mixed-level fractional factorial designs, two-level fractional factorial designs with hard-to-control factors, and supersaturated designs. Hamada and Wu proposed an iterative guided stepwise regression strategy for analyzing the data from such designs that allows entertainment of interactions. Their strategy provides a restricted search in a rather large model space, however. This article provides an efficient methodology based on a Bayesian variable-selection algorithm for searching the model space more thoroughly. We show how the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models. The proposed methodology is demonstrated with four examples, three of which come from actual industrial experiments.

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