Bias reduction via complementation of orthogonal arrays under a baseline parameterization

Under a baseline parameterization, minimum aberration orthogonal arrays minimize variance but not bias, while one-factor-at-a-time designs minimize bias but not variance. A new class of compromise designs is constructed by complementing and modifying minimum aberration arrays. The resulting information matrix is shown to have a compound-symmetric structure, and closed-form expressions are derived for the A s -, D s -, and E s -efficiency criteria. Simultaneous optimality under all three criteria is established within the class. A decomposition of the bias difference K 2 ( Z C 2 ∗ ) − K 2 ( Z MA ) into pairwise contributions reveals a sign-reversal mechanism in the alias matrix, and bias reduction relative to the parent design is proved for all regular fractions. Numerical results show bias reductions of 14%–49% with efficiency losses of only 1%–10%.