| In reality, a complex manufacturing process may often go wrong. It is essential to quickly detect the causes of malfunctioning once an out-of-control alarm is signaled. The goal of this thesis is to develop a model-based Bayesian fault diagnostic system and then apply the developed system to the data collected from very large scaled integrated circuit (VLSIC) manufacturing processes.;Controls are often the real cause of malfunctioning but they are difficult to be directly monitored. Instead, in-lines are usually observed to monitor processes since the abnormal behavior in controls can be reflected through the abnormal behavior of the in-lines. By studying the relationship between in-lines and controls, we can therefore make inference about controls based on in-lines. In this thesis, we use training data to model this relationship in both a linear regression model and a Gaussian process model (which is more suitable for non-linear behavior). The probabilistic inference on controls is made through the conditional distribution of controls given in-lines, which is obtained through Bayes theorem.;In theory, we develop a general framework for addressing the following questions in a Bayesian setting: (1) Which control is going out of control? (2) In what way is the control going wrong? (3) At what time does the control start to be in an abnormal condition? (4) By how much has the control gone wrong?;In practice, we implement the framework and apply it to simulated data as well as data collected from industry. Our results demonstrate that our Bayesian approach to fault diagnosis is of promising value in realistic applications. |
