Optimal crossover designs in a model with self and mixed carryover effects

We consider a variant of the usual model for crossover designs with carryover effects. Instead of assuming that the carryover effect of a treatment is the same regardless of the treatment in the next period, the model assumes that the carryover effect of a treatment on itself is different from the carryover effect on other treatments. For the traditional model, optimal designs tend to have pairs of consecutive identical treatments; for the model considered here. they tend to avoid such pairs. Practitioners have long expressed reservations about designs that exhibit such pairs and about the traditional model. The new model provides an attractive alternative that leads to appealing optimal designs.