Multiple Response Robust Design Of The Three Optimal Linear Regression

Experimental design is a technique for arranging experiments economically and scientifically based on the theories of probability and statistics,which has extensive application in industry producing and the engineering design. Robust design is an important branch and a hot topic of the experimental design.Recently,with the development of the theory of experimental design , robustness of a design has being increasingly concerned about by the experimental designers. In optimum design theory, many results have been obtained under the assumption of exactly correct response and homoscedasticity. But this assumption is not always correct. In most situations, an unknown bias or contamination may exist between the assumed response and the true response , so it's more dangerous to put the design obtained from the ideal model into practice. To reduce the risk, we consider the construction of designs for multiple approximately regression model,robust against unspecified contamination of the response function. We derive three criteria to obtain the robust optimal designs under the given model and then attain corresponding design density functions by the generalized least method and the variational method. Finally, we take a kind of dual-response models with two regressors as an example to illustrate how to get the detailed expression of the density functions and design points with using the method of random simulation.