A Case Study Involving Mixture–Process Variable Experiments within a Split-Plot Structure

ABSTRACT

When an experiment involves both mixture and process variables, the size of the experiment can increase dramatically and the assumption of complete randomization may be violated due to the cost or time to change some factor levels. In this situation, restrictions on the randomization of experimental runs are necessary, resulting in a split-plot structure. Furthermore, when some process variables are noise variables, it is important to consider the noise variables at the design stage of the process to find the robust parameter setting that makes the response “robust” to the variability transmitted from the noise factors. However, many mixture–process experiments are analyzed without considering this randomization issue. We provide a real example of a mixture–process experiment with noise variables within a split-plot structure. Our example demonstrates show to minimize the prediction error with noise variables in a situation where the standard analysis results in poor estimation for the prediction due to the restricted randomization. Without a proper analysis, the experiment leads to the wrong model and results in poor prediction. When the noise variables are ignored in the experiments, the model provides large random errors due to the effect of noise variables. We show that dual optimization using a mean model and a variance model can find the robust settings for the noise variables.

KEYWORDS:

• experimental design
• FDS plot
• mixture–process design
• noise variable
• optimality design
• robust parameter design
• split-plot design

Additional information

Notes on contributors

Tae-Yeon Cho

Tae-Yeon Cho holds a PhD in Industrial Engineering from Arizona State University. His area of interest is in quality and reliability engineering. He is focusing on design of experiments, response surface methodology, and mixture-process variable experiments. In 2005 and 2006, he received the Department Academic Commendations from the Industrial Engineering Department at ASU and Graduation Fellowship Award from the ASU Graduate College. He is a senior engineer in Samsung Electronics.

Douglas C. Montgomery

Dr. Douglas C. Montgomery is Regents' Professor of industrial engineering and statistics and Foundation Professor of Engineering at Arizona State University. His research and teaching interests are in industrial statistics. Professor Montgomery is a Fellow of the ASA, a Fellow of the ASQ, a Fellow of the RSS, a Fellow of IIE, a Member of the ISI, an Academician of the IAQ and has received several teaching and research awards.

Connie M. Borror

Dr. Connie M. Borror is a Professor in the Division of Mathematical and Natural Sciences at Arizona State University West. She earned her Ph.D. in Industrial Engineering from Arizona State University in 1998. Her research interests include experimental design, response surface methods, and statistical process control. She has co-authored two books and over 50 journal articles in these areas. Dr. Borror is a Fellow of the American Statistical Association and the American Society for Quality.