Three-level and mixed-level orthogonal arrays for lean designs

Orthogonal arrays (OA's) are widely used in design of experiments. Each OA has a specific number of rows that is fixed by the number of factors in the OA and the number of levels in each factor. In a practical application of an industrial experiment, however, because of various operational constraints it could happen that the number of runs of the experiment cannot be set exactly equal to the number of rows of an OA. In this case, a lean design can be used. A lean design is obtained by removing some specific rows and columns from the extended design matrix formed from an OA, so that the resulting sub-matrix still allows efficient estimation of the effects of some of the factors. Tables for 2-level lean designs are already available in the literature. In this paper, the authors will investigate 3-level lean designs and mixed-level lean designs, and construct tables for such designs for convenient use.