Model and Distribution-Robust Process Optimization with Noise Factors

Abstract

The uncertainty of the model form is typically neglected in process-optimization studies. In addition, not taking into account the existence of noise factors and nonnormal errors may invalidate the conclusions of such studies. In this paper, a Bayesian approach to model-robust process optimization in the presence of noise factors and nonnormal error terms is presented. Traditionally, in process optimization, methods such as the dual response approach are used in the presence of noise factors, and methods such as robust regression are used when the error terms are not normally distributed. Instead, this paper extends the recently proposed idea of model form-robustness using a Bayesian predictive approach to cases where there is uncertainty due to noise factors and due to the distributional assumptions of the errors. Two examples taken from the literature, one based on a factorial experiment and another based on a mixture experiment, are used to illustrate the proposed approach.

• Bayesian Optimization
• Response Surface Methodology
• Robust Parameter Design

Additional information

Notes on contributors

Ramkumar Rajagopal

Dr. Rajagopal is at Intel Corp. His email address is [email protected].

Enrique Del Castillo

Dr. del Castillo is Professor in the Department of Industrial & Manufacturing Engineering and Department of Statistics, Pennsylvania State University. His email address is [email protected].

John J. Peterson

Dr. Peterson is Director, Statistics in the Statistical Sciences Department. He is a member of ASQ. His email address is [email protected].