Building Equivalent Estimation Split-plot Designs for Response Surface Investigations

• Activity Number: 142
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Peter Parker*+ and Scott Kowalski and G. Geoffrey Vining
• Companies: NASA and Minitab, Inc. and Virginia Polytechnic Institute and State University
• Keywords: Split-Plot Designs ; Box-Behnken Designs ; Equivalent Estimation Designs ; Central Composite Designs

Abstract

Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Employing a split-plot design structure minimizes the number of times these hard-to-change factors are reset during the experiment. Recently, a class of second-order response surface split-plot designs 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 not a function of the variance components and can be obtained with standard statistical software. Moreover, design selection is robust to model misspecification and is independent of the error variance components. This paper reviews the conditions required to obtain an equivalent estimation design and outlines systematic design construction techniques to build these designs from the two most common families of completely randomized response surface designs: Central Composite and Box-Behnken. In addition, examples of equivalent estimation D-optimal and minimal-point designs are provided.