A Class of Experimental Designs for Estimating a Response Surface and Variance Components

This article introduces a new class of experimental designs, called split factorials, which allow for the estimation of both response surface effects (fixed effects of crossed factors) and variance components arising from nested random effects. With an economical run size, split factorials provide flexibility in dividing the degrees of freedom among the different estimations. For a split factorial design, it is shown that the OLS estimators for the fixed effects are BLUE and the variance component estimators from the mean squared errors on the ANOVA table are also minimum variance among unbiased quadratic estimators. An application involving concrete mixing demonstrates the use of a split factorial experiment.