Adaptive Order-of-Addition Experiments via the Quick-Sort Algorithm

The order-of-addition (OofA) experiment has received a great deal of attention in the recent literature. The primary goal of the OofA experiment is to identify the optimal order in a sequence of m components. All the existing methods are model-dependent and are limited to small number of components. The appropriateness of the resulting optimal order heavily depends on (a) the correctness of the underlying assumed model, and (b) the goodness of model fitting. Moreover, these methods are not applicable to deal with large m (e.g., m≥7). With this in mind, this article proposes an efficient adaptive methodology, building upon the quick-sort algorithm, to explore the optimal order without any model specification. Compared to the existing work, the run sizes of the proposed method needed to achieve the optimal order are much smaller. Theoretical supports are given to illustrate the effectiveness of the proposed method. The proposed method is able to obtain the optimal order for large m (e.g., m≥20). Numerical experiments are used to demonstrate the effectiveness of the proposed method.