A note on cyclic orthogonal designs

Orthogonality is considered to be one of the most important features for design of experiment. In this paper, we investigate orthogonal main-effect designs with cyclic structure in order to ensure the balance among all design columns. We show that such designs exist for any number of factors (k) and moreover, they are not unique. An explicit form for D-efficiency of cyclic orthogonal designs is derived. It is shown that D-optimal cyclic design essentially involves minimizing the tightness of the experimental range. The minimum tightness D-optimal cyclic orthogonal designs are presented and tabulated for k < 10.