Scalable level-wise screening experiments using locating arrays

Abstract

Alternative design and analysis methods for screening experiments based on locating arrays are presented. The number of runs in a locating array grows logarithmically based on the number of factors, providing efficient methods for screening complex engineered systems, especially those with large numbers of categorical factors having different numbers of levels. Our analysis method focuses on levels of factors in the identification of important main effects and two-way interactions. We demonstrate the validity of our design and analysis methods on both well-studied and synthetic data sets and investigate both statistical and combinatorial properties of locating arrays that appear to be related to their screening capability.

Keywords:

• algorithms
• analysis of designed experiments
• applications and case studies
• experimental design

Acknowledgements

The authors sincerely thank the editor and the referees for their valuable comments, which have greatly improved our paper.

We thank Stephen Seidel for writing the code to construct locating arrays and to analyze the data collected from their use in the experimentation. Thanks also to Isaac Jung for additional construction algorithms.

Data availability statement

The data that support the findings of this study are openly available at https://www.public.asu.edu/∼syrotiuk/tools.html.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Yasmeen Akhtar, Charles J. Colbourn, and Violet R. Syrotiuk was supported by the US National Science Foundation (NSF) under Grants NeTS-1813451 and NeTS-1421058. The work of John Stufken was supported by the US National Science Foundation (NSF) under Grants DMS-1935729 and DMS- 2304767.

Notes on contributors

Yasmeen Akhtar

Yasmeen Akhtar is an Assistant Professor at the Department of Mathematics, BITS Pilani K K Birla Goa Campus, India. She received her Ph.D. from the Indian Institute of Science Education and Research (IISER) Pune, India. She held postdoctoral positions at the Institute of Statistical Science, Academia Sinica, Taiwan, and the School of Computing, Informatics & Decision Systems Engineering (now the School of Computing and Augmented Intelligence), Arizona State University, USA. Her research interests include applied combinatorics and the design and analysis of experiments.

Fan Zhang

Fan Zhang is currently a Ph.D. candidate in the School of Mathematical and Statistical Sciences, Arizona State University. She received her B.S. degree in Statistics from the Beijing Normal University, China, in 2016, and M.S. degree in Statistics from the National Cheng Kung University, Taiwan, in 2018. Her research interests include design and analysis of experiments.

Charles J. Colbourn

Charles J. Colbourn earned his Ph.D. in 1980 from the University of Toronto in Computer Science. He has held academic positions at the University of Saskatchewan, the University of Waterloo, the University of Vermont, and is currently a Professor of Computer Science and Engineering at Arizona State University. Dr. Colbourn is the author of The Combinatorics of Network Reliability (Oxford) and Triple Systems (Oxford). He is editor-in-chief of the Journal of Combinatorial Designs. He edited The CRC Handbook of Combinatorial Designs. He is the author of about 400 refereed journal papers focusing on combinatorial designs and graphs with applications in networking, computing, and communications. He was awarded the Euler Medal for Lifetime Research (2003) and the Stanton Medal for Lifetime Service (2020) by the Institute for Combinatorics and its Applications.

John Stufken

John Stufken is a Professor of Statistics at George Mason University. His primary research interests include design and analysis of experiments and analysis of big data. He is a former Editor for the Journal of Statistical Planning and Inference and for The American Statistician. He held positions as Program Director for Statistics (National Science Foundation), Head of Department of Statistics (University of Georgia), Coordinator for Statistics (Arizona State University), and Director for Informatics and Analytics (University of North Carolina at Greensboro). He is an Elected Fellow of the Institute of Mathematical Statistics and the American Statistical Association and an Elected Member of the International Statistical Institute.

Violet R. Syrotiuk

Violet R. Syrotiuk is an Associate Professor of Computer Science and Engineering in the School of Computing and Augmented Intelligence at Arizona State University. Her research interests include applications of combinatorial design theory to computer networks, self driving networks, and programmable networks. Her work makes use of mid-scale experimental infrastructure including the new NSF FABRIC testbed. Dr. Syrotiuk serves on the editorial boards of Elsevier’s COMNET and COMCOM journals and is a TPC Co-Chair of IFIP Networking 2023.