Abstract
An order of addition experiment is a experiment that investigates how the order of addition of materials or components affects the results, with the primary objective of predicting and determining the optimal order of addition of reactants in an optimized reaction. Order of addition experiment are also commonly used in the medical field for drug combination therapy, where experimentation with all combinations of multiple drugs and their dosages is unaffordable due to cost considerations. To solve this problem, this paper proposes a new method of design table construction, combining the partial full order of addition design table and the two-level partial analysis factor design table to form a new class of design table by matrix product method. By adding the main factor and two-factor interaction effect terms and improving the corresponding additive model, we study the effects of factor effects and the order of addition effects of factors on the results under the order of addition experiment. We prove that the relative D-efficiency of the constructed one-class design table can reach 100% and solve an explicit expression for the D-efficiency of the full design. The superiority of the new method is demonstrated by comparing the simulation experiment with the relative D-efficiency of the random design table.