Computer-Generated Experimental Designs for Irregular-Shaped Regions

Abstract

This paper focuses on the construction of computer-generated designs on irregularly-shaped, constrained regions. Overviews of the Fedorov exchange algorithm (FEA) and other exchange algorithms for the construction of D-optimal designs are given. A faster implementation of the FEA is presented, which is referred to as fast-FEA (denoted FFEA). The FFEA was applied to construct D-optimal designs for several published examples with constrained experimental regions. Designs resulting from the FFEA are more D-efficient than published designs, and provide benchmarks for future comparisons of design construction algorithms. The construction of G-optimal designs for constrained regions is also discussed and illustrated with a published example.

Key Words:

• ACED
• DETMAX
• D-optimality
• Fedorov exchange algorithm
• genetic algorithm
• G-optimality
• mixture experiment
• optimal designs

Additional information

Notes on contributors

Nam-Ky Nguyen

Nam-Ky Nguyen He (http://turing.une.edu.au/nkn) received his Ph.D. in Agricultural Statistics at the Indian Agricultural Statistics Research Institute under Dr. Aloke Dey. He is currently a Senior Lecturer in the School of Mathematics, Statistics & Computer Science, University of New England, Australia. He is also the developer of the Gendex DOE toolkit (http://designcomputing.net/gendex). This toolkit is currently in use at more than 50 universities and research organizations worldwide. He has been working extensively in the area of computer-generated designs. He has about 30 publications in applied statistics /computing and collaborative research.

Greg F. Piepel

Greg Piepel He received his Ph.D. in Statistics at the University of Florida and is a Laboratory Fellow in the Statistical Sciences group at Battelle-Pacific Northwest Division in Richland, Washington, USA. He is also the developer of the MIXSOFT software and presents short courses on the design and analysis of mixture experiments (http://members.aol.com/mixsoft). His research interests are in the design and analysis of mixture and other constrained region experiments, optimal experimental design, statistical methods development, and solving applied problems in the physical and engineering sciences. Dr. Piepel is a Fellow of the American Statistical Association and is on the Editorial Review Board of the Journal of Quality Technology. He has published papers in Technometrics, Journal of Quality Technology, The American Statistician, Stats, Quality Engineering, Journal of the American Ceramic Society, Journal of Non-Crystalline Solids, and several other journals.