The General Balance Metric for Mixed‐level Fractional Factorial Designs

Mixed‐level designs are employed when factors with different numbers of levels are involved. Practitioners use mixed‐level fractional factorial designs as the total number of runs of the full factorial increases rapidly as the number of factors and/or the number of factor levels increases. One important decision is to determine which fractional designs should be chosen. A new criterion, the general balance metric (GBM), is proposed to evaluate and compare mixed‐level fractional factorial designs. The GBM measures the degree of balance for both main effects and interaction effects. This criterion is tied to, and dominates orthogonality criteria as well as traditional minimum aberration criteria. Furthermore, the proposal is easy to use and has practical interpretations. As part of the GBM, the concept of resolution is generalized and the confounding structure of mixed‐level fractional factorial designs is also revealed. Moreover, the metric can also be used for the purpose of design augmentation. Examples are provided to compare this approach with existing criteria. Copyright © 2008 John Wiley & Sons, Ltd.