A graphical method for evaluating the effect of blocking in response surface designs

Abstract

When fitting a response surface model, the least squares estimates of the model's parameters will generally depend on how the response surface design is blocked. Then, the choice of a blocking arrangement for a response surface design can have a considerable effect on estimating the mean response, on the size of the prediction variance and on the variance of the least squares estimator of the model's parameters. These are all shown to be affected by the sizes of the blocks and the allocation of experimental runs to the blocks. In this paper, we propose a graphical method for evaluating the effect of blocking in response surface designs. This graphical method can be used to examine how blocking influences the variance of the least squares estimator of the model's parameters. and to compare the effect of blocking in the cases of the orthogonal and nonorthogonal block designs, respectively

Keywords:

• response surface design
• orthogonal blocking
• fixed block effect: random block effect
• blocking effect variance plot
• total blocking variance
• total unblocking variance