Proposal Number: DMS 9803281 PI: Vijayan N. Nair, University of Michigan Mark H. Hansen, Bell Labs, Lucent Technologies Project: Statistical Methods for Process Control and Improvement in Advanced Manufacturing Abstract: This research project deals with methods for modeling, monitoring, diagnosis, and improvement of manufacturing processes with spatial data. The scope of the project goes beyond the traditional Shewhart's paradigm for statistical process control (SPC) which focuses primarily on process monitoring. A significant part of the research is the use of in-process and product quality data to develop failure diagnostics and to relate these to potential problems for process improvement. These issues are studied in the context of an integrated framework for process control and improvement. An overall strategy is proposed for using the spatial information in defect clustering as the basis for process improvement. The methodology consists of several parts. First, process monitoring methods for routinely monitoring the spatial data and detecting objects with significant clustering are developed. A Markov random field model with small-scale clustering is used to characterize ``in-control'' data. Statistical methods for failure diagnosis (signatures of spatial patterns) are obtained and the patterns are then related to process information for improvement. Various approaches for doing this including parametric models for large-scale clustering and formal methods based on classification are studied. Several other related topics, including modeling and analysis of ordinal data from temporal and spatial processes and the analysis of spatial data from designed experiments are also studied. These methods are developed and studied in the specific context of wafer map data in integrated circuit (IC) fabrication. Semiconductor manufacturing is one of the key manufacturing industries in the US, and hence statistical methods for process and yield improvement are clearly important from a practical viewpoint. However, the research issues and methods developed here are quite generic in nature and are of general interest to many other manufacturing processes with spatial data, including flat panel displays, printed circuit boards, and the manufacture and assembly of auto-bodies. These advanced manufacturing and high-technology industries all share the following features. Massive amounts of in-process and production data are now being collected routinely, made possible by advances in computing and data capture technologies. Much of these data have complex structures, in the form of spatial objects, images and so on. At the same time, competitive market pressures are placing a lot of emphasis on reducing product development cycle time. Moreover, process/product designers are operating on the boundaries of available subject matter knowledge of the underlying technology. Products are being manufactured and marketed before the technology is well-understood. These manufacturing processes are often not ``stable'', as is commonly assumed in the traditional statistical process control (SPC) paradigm. Thus, there is a critical need for statistical methods that exploit the extensive information available from in-process and product quality data not only for process monitoring but also for process improvement. The results from this research project will significantly advance methodology for the continuous improvement of advanced manufacturing processes.
