Multiple Response Linear Model Of The Compound Optimal Design

Experimental design is a technique for arranging experiments economically and scientifi-cally,based on the theories of probability and statistics,which has extensive application in indus-try producing and the engineering design. Optimal design is an important branch of the experi-mental design. It is designed as a pilot for the test purpose, through establishing the proper designcriteria and obtaining the optimal solution according to the design criteria.In practice, the models often have more than one response. Simultaneously, if faced withmultiple regression models are likely to be adopted,in order to make these models fitted withhigh efficiency, we can use the compound design to optimize the design. The study about abovetwo kinds of optimal design is obtained more attention, but a combination of two design researchdevelops relatively slow. Therefore, this article mainly studies D- and A- optimal criterion ofthe compound multiresponse linear model. Optimal criteria and equivalence theorem were es-tablished. With the covariance matrix known or not known, the article proposed new iterativealgorithm respectively, and find the optimal design through simulation.On the research of the optimal design based on D- optimal criterion, a general model isdefined. With the covariance matrix is known, we construct the compound D- optimal criteria andequivalence theorem. In a simple model, derived the optimal solution; If display solution can notbe found, we use given iterative algorithm. We get the answer through Matlab.On the research of the optimal design based on A- optimal criterion, the equivalence theoremis constructed. No matter the covariance matrix is known or not, the optimal design of com-pound structures is given through iterative algorithm. In both cases, numerical examples are givenrespectively to verify the feasibility of iterative algorithms.Consequently, the paper has deep researches on several areas of compound designs for multi-response linear models. More arguments are required with the development of optimal design.