Efficient minimal balanced cross-over designs in higher-order carryover effects

Experimenters have limited flexibility in their choice of cross-over designs, in terms of, number of treatments, subjects, and repeated measurements. Also, cross-over design balanced with higher-order carryover effects presented in the literature requires a large number of experimental subjects, which is impractical for its implementation. Most experimental studies demand a smaller number of subjects, which is possible only in a minimally balanced cross-over design. In this article, two simple methods have been presented, which construct minimal balanced cross-over designs having less, equal, and more periods than the number of treatments. The first method constructs cross-over designs with more periods, while the second method constructs cross-over designs with less or equal periods. As a result, four new families of cross-over designs have been obtained, in which one family of cross-over designs has periods greater than the number of treatments, two families of cross-over designs have three periods, and one family of cross-over designs has periods equal to the number of treatments. All the designs possess good efficiency of separability, and therefore they are suitable for the estimation of treatments and first-second carryover effects of treatments at lower cost of experiments due to a smaller number of experimental subjects as compared to the designs available in the literature.