Universally optimal balanced changeover designs with first residuals

Considering the presence of first order residual effects of treatments, a family of variance balanced changeover designs has been presented and universal optimality of the designs is established. The designs use only v experimental units and (v ? 1)/2 periods for v = 4t + 3 prime or prime power number of treatments; t being a positive integer. A special feature of the proposed designs is that ‘in the order of presentation of treatments to experimental units over periods, each treatment is once immediately preceded by only half of the other treatments and is immediately followed once by the remaining half of the treatments’. This characteristic results in reducing the size of the variance balanced designs considerably.