The construction of nearly balanced and nearly strongly balanced uniform cross-over designs

In this paper we consider the class of uniform cross-over designs. Existing results on the universal optimality of uniform cross-over designs are reviewed and a general method of construction is described. The constructed designs fall into four families, which include the balanced and strongly balanced designs as special cases: the remaining designs we refer to as nearly strongly balanced, a term first introduced by Kunert (Ann. Statist. 11 (1983)), and nearly balanced. The nearly strongly balanced and nearly balanced designs form an important family of uniform cross-over designs which provide designs where balanced or strongly balanced designs do not exist. The construction method can be easily generalized for any number of periods and subjects, as long as they are both a multiple of the number of treatments. Some illustrative examples are included.