Connectedness and orthogonality in multi-factor designs

Under the usual additive model, a design of n factors at levels mi (i = 1, …, n) is defined to be connected if the rank of its information matrix is equal to Σmi−n+1. The ith factor is said to be connected if the coefficient matrix of the reduced normal equations obtained by eliminating all other factors has rank mi−1. This paper obtains lsimple necessary and sufficient conditions for connectedness. This is achieved by restricting the class of designs under consideration through the concept of orthogonality between pairs of factors. The degree of restriction imposed on the class of designs is mild, and some interesting and practical results are obtained.