Exact Inference for Response Surface Designs Within a Split-Plot Structure

Abstract

Many industrial experiments involve factors that are hard to change as well as factors that are easy to change, which leads naturally to split-plot experiments. Unfortunately, the literature for second-order response surface designs traditionally assumes a completely randomized design. By carefully choosing the design for response surface experiments, it is possible to guarantee that the ordinary least-squares estimates of the model are equivalent to the generalized least-squares estimates. This paper uses designs satifying this result to derive conditions for exact tests of almost all of the model parameters. It then sets up the Satterthwaite's procedure for the remaining parameters. An example illustrates the methodology. Comparisons between the exact estimators, estimators based on replicated points, and estimators using restricted maximum likelihood estimators (REML) are done using the example.

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