The ordering effect of sequential treatment addition is present in many problem areas ranging from online search ranking and job scheduling to election standardization and the design of clinical trials. The straightforward approach to studying this ordering effect on a response is to test each permutation of the treatment components. When the run size becomes too costly, a random sample of permutations can instead be used for estimation and inference. Noting the inefficiencies present in both of these approaches, well-designed order-of-addition experiments have been proposed to reduce the computational complexity of studying the ordering effect without sacrificing statistical power; however, this problem is under-studied in the statistical literature.