Crossover designs are common for experiments in many scientific disciplines, for example psychology, pharmaceutical science, and medicine.
Most clinical trials are analyzed using repeated-measurements ANOVA (analysis of variance) or mixed models that include random effects.
In most longitudinal studies of human subjects, patients may withdraw from the trial or become "lost to follow-up".
In a controlled, randomized crossover designs, such imbalances are implausible (unless covariates were to change systematically during the study).
Optimal crossover designs are discussed in the graduate textbook by Jones and Kenward and in the review article by Stufken.
However, planning for sufficiently long wash-out periods requires expert knowledge of the dynamics of the treatment, which is often unknown.