On invariance and randomization under factor permutation in fractional factorial designs

This paper establishes the spectrum invariance of the information matrix under an arbitrary subgroup Г of the group Δ of factor permutations. In addition, it provides the randomized unbiased estimation of a linear parametric function under the composition Ω°Г, where Ω is the group of level permutations. These two results are achieved for the most practical partitioning of the whole parametric vector using the concepts of Г-closed and admissibility of a parametric subvector. Applications are given with an explicit illustration using the minimal resolution III design setting for the 2³ factorial.