  We present a new "grey-box" approach to anomaly detection in smart
manufacturing. The approach is designed for tools run by control systems which
execute recipe steps to produce semiconductor wafers. Multiple streaming
sensors capture trace data to guide the control systems and for quality
control. These control systems are typically PI controllers which can be
modeled as an ordinary differential equation (ODE) coupled with a control
equation, capturing the physics of the process. The ODE "white-box" models
capture physical causal relationships that can be used in simulations to
determine how the process will react to changes in control parameters, but they
have limited utility for anomaly detection. Many "black-box" approaches exist
for anomaly detection in manufacturing, but they typically do not exploit the
underlying process control. The proposed "grey-box" approach uses the
process-control ODE model to derive a parametric function of sensor data.
Bayesian regression is used to fit the parameters of these functions to form
characteristic "shape signatures". The probabilistic model provides a natural
anomaly score for each wafer, which captures poor control and strange shape
signatures. The anomaly score can be deconstructed into its constituent parts
in order to identify which parameters are contributing to anomalies. We
demonstrate how the anomaly score can be used to monitor complex multi-step
manufacturing processes to detect anomalies and changes and show how the shape
signatures can provide insight into the underlying sources of process variation
that are not readily apparent in the sensor data.
