Design construction and model selection for small mixture-process variable experiments with high-dimensional model terms

Abstract

This paper considers the design construction and model selection for mixture-process variable experiments where the number of variables is large. For such experiments the generalized least squares estimates cannot be obtained and hence it will be difficult to identify the important model terms. To overcome these problems, here we employ the generalized Bayesian-D criterion to choose the optimal design and apply the Bayesian analysis method to select the best model. Two algorithms are developed to implement the proposed methods. A fish-patty experiment demonstrates how the Bayesian approach can be applied to a real experiment. Simulation studies show that the proposed method has a high power to identify important terms and well controls the type I error.

Keywords:

• Bayesian
• D-optimality criterion
• generalized Bayesian-D criterion
• split-plot design

Acknowledgments

The authors thank two anonymous referees for their many helpful comments and suggestions that led to substantial improvements to this article.

Additional information

Notes on contributors

Kashinath Chatterjee

Kashinath Chatterjee is an Adjunct Professor of the Division of Biostatistics and Data Science at the Augusta University, Georgia. His research interests include experimental and optimal designs, statistical quality control, reliability analysis, and robust parameter design.

Chang-Yun Lin

Chang-Yun Lin is a professor at the Department of Applied Mathematics and the Institute of Statistics at National Chung Hsing University, Taiwan. He received his Ph.D. from National Tsing Hua University in Taiwan in 2009 and worked in high-tech manufacturing plants for 7 years. His research areas involve experimental design, machine learning, deep learning, Bayesian analysis, and genetic statistics.