A blocked staggered-level design for an experiment with two hard-to-change factors

Abstract

Staggered-level designs have been introduced in the literature as cost-efficient and statistically efficient alternatives to split-plot and split-split-plot designs for experiments with multiple hard-to-change factors. In this article, we present an application of a staggered-level design to a staple fiber cutting process at Eastman. The experiment was run in blocks and involved one quantitative hard-to-change factor, one two-level categorical hard-to-change factor, and three quantitative easy-to-change factors. We review existing work on staggered-level designs, discuss D-, A- and I-optimal staggered-level designs and blocked staggered-level designs, and perform an analysis of the data from the staple fiber cutting experiment.

Keywords:

• A-optimal design
• blocking
• D-optimal design
• I-optimal design
• split-plot design
• split-split-plot design

Acknowledgements

We are grateful to the three development engineers at Eastman, Kevin Barham, Jessica Remmert, and Yubin Shen, who executed this experiment. It was their dedication to the planning and rigorous collection of experimental data that made the application of the staggered-level design a success.

Data availability statement

The data supporting the findings reported in this article are available within the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Peter Goos

Peter Goos is a full professor at the Faculty of Bio-Science Engineering of KU Leuven, and at the Faculty of Business and Economics of the University of Antwerp, where he teaches various introductory and advanced courses on statistics and probability. His main research area is the statistical design and analysis of experiments. Besides numerous influential articles in various kinds of scientific journals, he published the books The Optimal Design of Blocked and Split-Plot Experiments, Optimal Experimental Design: A Case Study Approach, Statistics with JMP: Graphs, Descriptive Statistics and Probability and Statistics with JMP: Hypothesis Tests, ANOVA and Regression. For his work, Peter Goos has received four Shewell Awards, two Lloyd S. Nelson Awards, the Youden Award and a Brumbaugh Award from the American Society for Quality, the Ziegel Award and the Statistics in Chemistry Award from the American Statistical Association, and the Young Statistician Award of the European Network for Business and Industrial Statistics (ENBIS). Peter Goos is also a co-founder of EFFEX™ which provides software for the design of experiments and the analysis of experimental data.

Katherine Brickey

Katherine Brickey is a statistician at Pfizer. Prior to joining Pfizer, she worked for seven years as a statistician at Eastman. In her work she commonly uses statistical methods such as design and analysis of experiments, statistical process control, and other modeling solutions. She serves as chair-elect for the American Society for Quality Chemical and Process Industries Division. Katherine holds a master's degree in statistics from Virginia Tech.

Ying Chen

Ying Chen holds an M.Sc. in Statistics and Data Science and is a doctoral researcher at the Department of Biosystems, KU Leuven, Belgium. Her areas of interest include design of experiments, statistical modeling, and numerical optimization.