Fractional Box–Behnken Designs for One-Step Response Surface Methodology

Abstract

In contrast with the usual sequential nature of response surface methodology (RSM), recent literature has proposed both screening and response surface exploration using a single three-level design; this approach is known as “one-step RSM”. We discuss and illustrate two shortcomings of the current one-step RSM designs and analysis. Subsequently, we propose a class of three-level response surface designs, constructed by taking subsets of Box–Behnken designs, that will address these shortcomings and aid the user in being appropriately advised as to factor importance. We illustrate the designs and analysis with simulated and real data.

• Effect Heredity
• Effect Sparsity
• Incomplete Block Design
• One-Step RSM
• Subset Design

Additional information

Notes on contributors

David J. Edwards

Dr. Edwards is Assistant Professor of Statistics in the Department of Statistical Sciences and Operations Research. He is a member of ASQ. His email address is [email protected].

Robert W. Mee

Dr. Mee is Professor of Statistics in the Department of Statistics, Operations, and Management Science. He is a member of ASQ. His email address is [email protected].