Abstract: Varying coefficient Regression theory is applied to the discussion on quality characteristic influenced by factors’ mutuality during the process of multifactor test.In order to find the optimal combination of factor levels,the effect of other factors is changed by adjusting the coefficient variable.The paper studies varying coefficient regression theory in robust design,builds quality characteristic mean model and variance model and gets an optimal combination of factor levels.The feasibility of the theory is illustrated by the ink printing.

Key words: variable coefficient model, nonparametric regression, robust design, cross validation