Abstract: A model of additional experiment is suggested with n factors and up to n-1 interactions, when a certain set of constrained conditions is met, it can be proved by the incomplte-sum operator that the estimates of ensemble mean and all interactions and observation errors are defintiely unique. Meanwhile, it can be shown further that the calculation of all interreactions forms a recursive algorithm, which can be easily applied to a complex system for testing the significance of the factors and determining the optimal engineering conditions.