Construction of Balanced Equivalent Estimation Second-Order Split-Plot Designs

Abstract

Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Using a split-plot design (SPD) structure reduces the number of times that these hard-to-change factors are reset during the experiment. A class of second-order response surface SPDs has been proposed in which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Equivalent estimation designs provide best linear unbiased estimates that are independent of the variance components and can be obtained with standard statistical software. Moreover, design selection is robust to model misspecification and does not require previous knowledge of the variance components. This article expands the conditions to obtain equivalent estimation designs and outlines two systematic design construction techniques for building balanced versions of the central composite design. In addition, it presents an approach to generating equivalent estimation D-optimal designs. By applying these design construction techniques, a catalog of designs is generated. These methods provide practitioners with the necessary tools to build equivalent estimation SPDs for a wide variety of applications.