Some optimal criteria of model-robustness for two-level non-regular fractional factorial designs

We present some optimal criteria to evaluate model-robustness of non-regular two-level fractional factorial designs. Our method is based on minimizing the sum of squares of all the off-diagonal elements in the information matrix, and considering expectation under appropriate distribution functions for unknown contamination of the interaction effects. By considering uniform distributions on symmetric support, our criteria can be expressed as linear combinations of $B_s(d)$ characteristic, which is used to characterize the generalized minimum aberration. We give some empirical studies for 12-run non-regular designs to evaluate our method.

💡 Research Summary

This paper addresses the problem of evaluating and optimizing model‑robustness for non‑regular two‑level fractional factorial designs. While regular designs benefit from well‑established criteria such as minimum aberration or D‑optimality, non‑regular designs lack a clear quantitative measure of how vulnerable they are to model misspecification, especially when unmodelled high‑order interaction effects (“contamination”) are present. The authors propose a new robustness criterion that directly targets the information matrix of the design.

The core idea is to minimize the sum of squares of all off‑diagonal elements of the information matrix (X’X): \