Study Of Two Classes Of Composite Designs

Experimental designs and analysis is one of the important branches of math-ematical statistics,it is used widely in many fields including industry,agriculture,medical science,physics and astronomy.In practice,study of a process or system often focuses on the relationship between the response and the input factors,its purpose can be to optimize the response.Response surface methodology(RSM)is an effective tool for exploring the relationships between the response and the fac-tors,and the common way that researchers address response surface methodology in the literature is to use central composite designs(CCDs).Central composite designs can be used to screen factors and build response surface models.In recent years,some new composite design ideas have been proposed,for example,a new class of composite designs based on orthogonal arrays,called orthogonal array composite designs(OACDs).This new class of composite designs inherit the good mathemati-cal structure of orthogonal array and have some desired features,they can also used to screen factors and build models effectively.Some statistician study the desired features of orthogonal array composite designs,especially comparing to the central composite designs under second-order polynomial model.But these researches were discussed when star points value ?=1,for general a was not considered.In this paper,we will continue to study the two classes of composite designs,discussing the D-efficiencies for estimating the parameters for general a under the second-order model and obtain some theoretical results.Moreover,the determination of a value for star points will be discussed from the perspective of space-filling and we proposed a new criteria to determine the a value,that is calculating the centered L2-discrepancy to measure the uniformity of designs,then find the ? value to make the design more uniformly.Last,discussing the application of composite designs in the robot'arms and comparing the two classes of composite designs.