Two-Stage Experimental Design for Multiple Objectives

Abstract The D -optimal design for the nonlinear model typically depends on the unknown parameters to be estimated.Therefore, it is strongly recommended in literature to use a sequential experimental design for estimating theparameters. In this paper two stage experimental design is discussed under many different circumstancesincluding estimating parameters. The method is so universal to be applied to any mixture of objectivesfor any model including linear model. A hybrid approach is suggested to handle more than 2 objectives intwo-stage experimental design. The design is discussed in approximate design framework.Keywords: D -optimal design, sequential experimental design, two-stage experimental design. 1. 서론 반응변수 y ( x )는 식(1.1)과 같이 x 의비선형 함수로 연결되어 있다. y = η ( x,θ ) + ϵ, (1.1)여기서 θ T = ( θ 1 ,...,θ p )는 추정하여야 할 모수벡터이다. 실험설계 ξ 는 실험영역 Ω 내의유한 k 개의점 x i 2 Ω, i = 1 , 2 ,...,k 에 대한 확률질량함수 ξ ( x i ), i = 1 , 2 ,...,k 로 기술된다. 개개의 ξ ( x i ), i = 1 , 2 ,...,k 는 n i /n 의형태를 가지며∑ ki ξ ( x i ) = 1