Construction Of Two-level Component Orthogonal Arrays For Order-of-Addition Experiments

An order-of-addition（Oof A）experiment is a kind of experiment in which the mea-sured response depends on the order of adding m different materials or components into the system.At present,the two mainstream methods for constructing schemes for Oof A experiment are pair-wise ordering design and component orthogonal design.Component orthogonal arrays（COAs）,as subsets of all possible permutations on experimental factors,are suitable for collecting data from order-of-addition experiments due to their pairwise balance property between any two positions of the orders.When the levels of components can be changed（E.g.,high level and low level）,the standard statistical design method has been to use the Cartesian product design,which often results in a large number of experimental runs.To reduce the number of runs,in this paper,we propose combining COAs and 2^m-pfactional factorial designs by using Subcartesian product.Two systematic method are given for design construction.Specifically,in Construction 1,the COA is sliced into r symmetric U designs,and the 2^m-pdesign is randomly sliced into r groups of equal size,where r is the maximum common factor of the number of experiments of the two designs,and then combined by Subcartesian product.When m is a prime power,the COA required in construction 1 can be obtained by juxtaposing m-1 mutually orthogonal m-pth Latin squares.In construction 2,the COA is randomly sliced into r groups of equal size,and the 2^m-pdesign is sliced into r symmetric U designs,which are then combined by Subcartesian product.The 2^m-pdesign required in construction 2 can be obtained by fold-over technology,or when the defined word length of a column of the 2^m-pdesign is odd,it also satisfies.In this dissertation,it is further showed that the order-of-addition factorial design obtained by the above construction method is a factorial component orthogonal design.The number of runs obtained by the Subcartesian product method is usually much smaller than that obtained by the Cartesian product method.In addition,the constructed design satisfies the pairwise balance property and has the same D-efficiency as the full m!×2^m design under the main-effect model.Finally,computer simulation experiments show that under the premise of the same number of experiments,the properties of the design searched by the coordinate exchange algorithm with the goal of improving D-efficiency are largely inferior to the factorial orthogonal design components obtained by the construction method of this thesis.