Classification of strength-three multi-level orthogonal arrays

Generalized Aberration (GA) is one of the most frequently used criteria to quantify the suitability of an orthogonal array (OA) to be used as an experimental design. We demonstrate that this criterion is less suitable than other criteria to classify multi-level OAs of strength 3. For this purpose, we classified complete series of three-level strength-3 OAs with 54 and 81 runs using the GA criterion, the estimation capacity, the projection estimation capacity, the rank of the second-order model matrix, the D-efficiency for a model with all the main effects and all the two-factor interactions, and a new model-robustness criterion. For all of the series, we provide a list of admissible designs according to the criteria of interest.