The statistical modeling of multistage sequential manufacturing processes requires models both for processes running as desired and for processes suffering from faults. In addition, tools are needed for monitoring and controlling the process, for diagnosing faults, and for predicting future data. This research project is developing such models and tools. A starting point is a hierarchical mixture of recursive regression models with Markov transition structure having the faulty processes as absorbing states. Developing the models requires understanding the sensitivity of predictions to the parameters of the models. For example, the use of absorbing states for faulty processes, although intuitively appealing and mathematically simple, does lead to some undesirable results that need to be addressed. Prediction requires numerical methods for adequately summarizing uncertainty from many sources. In particular, it is often necessary to predict yield several stages in the future for an ongoing process, and the marginal distributions for the output are not available in closed form. Monitoring ongoing processes requires the development of appropriate summary statistics and displays. Diagnosis and monitoring both require the ability to partition uncertainty amongst several competing possibilities (such as different possible faults) and make decisions based on the relative costs of the possible errors. %%% The research develops a general framework for modeling multistage sequential manufacturing processes. The framework facilitates monitoring of ongoing processes, prediction of future and current yield, and diagnosis of faults. In a multistage process with in-line measurements, information becomes available sequentially and one needs to update one's state of knowledge as the information arrives. This leads naturally to the use of a Bayesian statistical approach to the modeling of uncertainties in such a process. The process level problems addressed by this research are those of in-line measurement choice, control chart construction, learning about immature processes, and process control. The research will lead to more sensitive monitoring tools and more comprehensive prediction and diagnosis tools that should help to improve the competitiveness of American manufacturers in high technology areas such as very large scale integrated circuit production. ***
