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.