Stability conditions and robustness analysis of a general MMSE run-to-run controller

Abstract

Run-to-run (R2R) control plays a vital role in monitoring or adjusting the manufacturing process of integrated circuits. In this article we propose a generalized quasi-MMSE controller for a process whose Input-Output (I-O) model follows a general Transfer Function (TF) model with ARIMA disturbance and analytically derive the long-term stability conditions and their limiting distribution. Furthermore, we use a comprehensive simulation study to compare the control performances among several potential controllers when the process I-O model follows a TF model of order (2, 2, 0) with ARIMA disturbance of order (2, 1, 2). The results demonstrate that using improper controllers may seriously affect the control performance in terms of the long-term stability conditions and the short-term total mean squared error. Supplementary materials are available for this article. Go to this article’s online edition of IIE Transactions for Appendices.

Keywords:

• Run-to-run control
• dynamic system
• quasi-MMSE controller
• process disturbance
• transfer function model

Additional information

Notes on contributors

Sheng-Tsaing Tseng

Sheng-Tsaing Tseng is a professor of the Institute of Statistics at Tsing-Hua University. He received a Ph.D. in Management Science from Tamkang University, Taiwan. His research interests include quality and productivity improvement and reliability lifetime analysis. His articles have appeared in IIE Transactions, Technometrics, Journal of Quality Technology, Naval Research Logistics, International Journal of Production Research, European Journal of Operational Research, IEEE Transactions on Reliability, Reliability Engineering & System Safety, IEEE Transactions on Semiconductor Manufacturing, Journal of Statistical Planning and Inference, and other technical journals. He is an elected member of ISI and a senior member of ASQ. Currently, he serves as an Associate Editor of Technometrics.

Fugee Tsung

Fugee Tsung is a professor of the Department of Industrial Engineering and Decision Analytics (IELM), Director of the Quality and Data Analytics Lab, at the Hong Kong University of Science and Technology (HKUST). He is a Fellow of the Institute of Industrial and systems Engineers (IISE), Fellow of the American Society for Quality (ASQ), Fellow of the American Statistical Association (ASA), Academician of the International Academy for Quality (IAQ) and Fellow of the Hong Kong Institution of Engineers (HKIE). He is Editor-in-Chief of Journal of Quality Technology (JQT). He has authored over 100 refereed journal publications, and is the winner of the Best Paper Award for the IIE Transactions in 2003, 2009, and 2017. He received both his M.Sc. and Ph.D. from the University of Michigan, Ann Arbor and his B.Sc. from National Taiwan University. His research interests include industrial big data and quality analytics.

Jo-Hua Wu

Jo-Hua Wu received an M.S. degree in Statistics from National Tsing-Hua University, Taiwan, in 2017. She is currently a data scientist at Acer Incorporated. She research interests include run-to-run (R2R) process control, time series analysis, biomedical signal analysis, and modeling through methods of statistics and machine learning.