A class of response surface split-plot designs

Abstract

There are many situations in industrial experimentation where departures from the fundamental principles of experimentation—randomization, replication, and local control of error—are commonplace. For instance, complete randomization is not always feasible when factor level settings are hard, impractical, or inconvenient to change, or when the resources available to execute the experiment under homogeneous conditions are limited. These restrictions in randomization lead to split-plot designs. Often, we are also interested in fitting higher-order statistical models, which calls for response surface split-plot designs. In this article we explore the systematic construction of a class of response surface split-plot design we call response surface Cartesian product split-plot designs. This collection of design alternatives offers an effective and efficient addition to the split-plot design repertoire available currently in the engineering, manufacturing, quality control, and test and evaluation communities. These designs are generally competitive in size relative to other standard designs, easy to construct, can be executed sequentially, have good coverage, low prediction variances, minimal aliasing between the model terms, and are suitable for cuboidal and spherical regions of the factor space. When evaluated with well-accepted design evaluation criteria, response surface Cartesian product split-plot designs perform as well as designs that have been standards in the response surface split-plot methodology community such as equivalent estimation designs, minimum whole plot designs, and optimal designs.

Keywords:

• Cartesian product split-plot designs
• design of experiments
• response surface split-plot designs
• response surface methodology
• split-plot designs

Additional information

Notes on contributors

Luis A. Cortés

Luis A. Cortes is a Principal Test Engineer at Huntington Ingalls Industries - Technical Solutions Division and a former MITRE Corporation and U.S. Navy Civilian. He earned a BS in Chemical Engineering from University of Puerto Rico, an MS in Mechanical Engineering from California State University Los Angeles, a PhD in Mechanical Engineering from Colorado State University, and graduated from the US Naval Material Command Civilian Logistics Intern Program in Quality and Reliability. He is Senior Member of the American Society for Quality and a member of the International Test and Evaluation Association. His research interests include split-plot designs, response surface methods, modeling and simulation, and test design and analysis.

James R. Simpson

James R. Simpson is a Principal at JK Analytics and a former Professor in the Department of Industrial Engineering at Florida State University and Florida A&M University. He earned a BS in Operations Research from the United States Air Force Academy, an MS in Operations Research from the Air Force Institute of Technology, and a PhD in Industrial Engineering from Arizona State University. He is Editor Emeritus for Quality Engineering and served as Chair of the ASQ’s Publications Management Board. He is a member of American Statistical Association, and a Fellow of the American Society for Quality. His research interests include design and analysis of experiments, simulation, response surface methods, applied optimization, regression analysis, and quality control.

Peter A. Parker

Peter A. Parker is a Team Lead in the Advancement Measurement System Branch at the NASA’s Langley Research Center and serves an Agency-wide statistical expert. He earned a BS in Engineering from Old Dominion University, an MS in Applied Physics and Computer Science from Christopher Newport University, and both and MS and PhD in Statistics from Virginia Polytechnic Institute and State University. He is a member of the American Statistical Association, Senior Member of the American Society for Quality, and Senior Member of the American Institute for Aeronautics and Astronautics. Pete serves as the Chair of the ASQ’s Publications Management Board. He is Editor Emeritus for Quality Engineering. His expertise is in collaboratively integrating research objectives, measurement sciences, test design, and statistical methods to produce actionable knowledge for aerospace research and development.