A Measure for Evaluating the Effect of Blocking in Response Surface Designs Using Cuboidal Regions

입방형 영역을 사용한 반응표면계획에서 블록효과를 평가하기 위한 측도

The fitting of a response surface model and the subsequent exploration of the response surface are usually based on the assumption that the experimental runs are carried out under homogeneous conditions. This, however, may be quite often difficult to achieve in many experiments. To control such an extraneous source of variation, the response surface design should be arranged in several blocks within which homogeneity of conditions can be maintained. In this case, when fitting a response surface model, the least squares estimates of the model's parameters and the prediction variance will generally depend on how the response surface design is blocked. That is, the choice of a blocking arrangement for a response surface design can have a considerable effect on estimating the mean response and on the size of the prediction variance. In this paper, we propose a measure for evaluating the effect of blocking of response surface designs using cuboidal regions.