Using Individual Factor Information in Fractional Factorial Designs

While literature on constructing efficient experimental designs has been plentiful, how best to incorporate prior information when assigning factors to the columns of a nonregular design has received little attention. Following Li, Zhou, and Zhang (2015), we propose the individual generalized word length pattern (iGWLP) for ranking columns of a nonregular design. Taking examples from the literature of recommended orthogonal arrays, we illustrate how iGWLP helps to identify important differences in the aliasing that is likely otherwise missed. Given the complexity of characterizing partial aliasing for nonregular designs, iGWLP will help practitioners make more informed assignment of factors to columns when using nonregular fractions. We provide theoretical justification of the proposed iGWLP. A theorem is given to relate the proposed iGWLP criterion to the expected bias caused by model misspecifications. We also show that the proposed criterion may lead to designs having better projection properties in the factors considered most likely to be important. Furthermore, we discuss how iGWLP can be used for design selection. We propose a criterion for choosing best designs when the focus is on a small set of important factors, for which the aliasing of effects involving these factors is minimized.