Optimal Fractional Factorial Plans for Main Effects Orthogonal to Two-Factor Interactions: 2mSeries

This article develops some theory of balanced 2m fractional factorial designs which permit estimation of main effects orthogonally to two-factor interactions and the general mean, whose size N is desirably small and which are optimal with respect to the three standard criteria namely, the trace, determinant and the largest root of the variance-covariance matrix of the estimates. The equivalence of these criteria is established for certain situations. For various practical values of m and N, balanced designs are obtained, some of which are also shown to be optimal.