Abstract

In Fisher (1971), a lady was able to distinguish (by tasting) from whether the tea or the milk was first added to the cup. This is probably the first popular Order of Addition (OofA) experiment. In general, there are m required components and we hope to determine the optimal sequence for adding these m components one after another. It is often unaffordable to test all the m! treatments (for example, m!=10! is about 3.5 millions), and the design problem arises. We consider the model in which the response of a treatment depends on the pairwise orders of the components. The optimal design theory under this model is established, and the optimal values of the D-, A-, E-, and M/S-criteria are derived. For Model-Free approach, an efficient sequential methodology is proposed, building upon the basic concept of quick-sort algorithm, to explore the optimal order without any model specification. The proposed method is capable to obtain the optimal order for large m (≥ 20). This work can be regarded as an early work of OofA experiment for large number of components. Some theoretical supports are also discussed. One case study for job scheduling will be discussed in detail.