Measures for evaluating the lotted of blocking in response surface designs

Abstract

The conditions under which experimental trials are performed in a response surface design may not, in general, be homogeneous. In this case, blocking may be usually carried out for within-block homogeneity. When fitting a response surface model, the estimates of the mean response and its prediction variance generally depend on the way a given 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. Therefore, care should be exercised in the selection of blocks. In this paper, we propose measures for evaluating the effect of blocking in response surface designs in terms of prediction variance when block effects are fixed. These measures can be used as useful tools to examine how blocking influences the prediction variance, and to compare the effect of blocking on the prediction variance in the cases of the orthogonal and non-orthogonal block designs under the given experimental region, respectively.

Keywords:

• prediction variant
• nrthngnnal blocking: resion moment
• average increase in the prediction variance(AIPV)
• spherical region moment
• blocking effect