Comparison Of Projection Properties On Two Types Of Order-of-Addition Experimental Designs

Order-of-addition experiment,as a special type of experiment,uses a series of experiments to determine the optimal addition order of materials or variables.Therefore,it has been widely used in many fields including medicine,chemical industry,biology and agriculture and so on.In the actual experimental procedure,if too many materials need to be added,it is impossible to perform the full design with all possible permutations.Order-of-addition orthogonal arrays and component orthogonal arrays are two kinds of designs for order-of-addition experiments.Such designs have good theoretical properties and application with relatively small number of runs.Accordingly,they have been extensively discussed in order-of-addition experimental domain.At present,the literature mostly focuses on the properties,search and construction strategies of the two types of designs.From the perspective of practical application,this paper first proposed the concept of order-of-addition projection design,furthermore,discussed and compared the properties of the two designs and their corresponding projection designs from the aspects of D-efficiency and balance.The research results show that under the given number of components,order-ofaddition orthogonal arrays and their projection designs can achieve good performance in the pairwise ordering model,but the performance in the component-position model is not robust enough;the improved component orthogonal array has relatively good performance under both models.The column permutation method proposed by Yang,Sun and Xu(2020)is adpoted to give the component orthogonal arrays that achieve the optimal D-efficiency and have the best dimensional projection properties under two models.Moreover,through a drug combination experiment,this paper verifies that a design with good projection properties can retain more information after ignoring a small amount of components,thus ideal fitting and prediction performances are achieved under serveral models.Finally,the idea of model averaging is introduced.The S-AIC method and other model weight determination methods further reduce the prediction mean squared error.