Gaussian Mixture Model for Anomaly Detection in Semiconductor Manufacturing
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Solution Overview
Problem
Anomaly detection in non-stationary systems, such as semiconductor manufacturing, is challenging due to the difficulty in effectively identifying outliers and improving the quality and yield of individual unit processes using simple statistical approaches.
Innovation Solution
A method involving the determination of a Gaussian mixture model (GMM) to compute anomaly scores for variables in semiconductor manufacturing processes, allowing for the identification of outliers and subsequent modification of process variables to enhance quality and yield, utilizing a combination of Gaussian mixture models, temporal-coupling multi-modal mixture models, and sparse graphical models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If simple statistical approaches are used for anomaly detection, then the method is easy to implement, but the detection precision is insufficient for non-stationary systems
Solution Approach 1:
The patent transforms the anomaly detection problem by changing the parameter representation from raw process values to anomaly scores derived from Gaussian mixture models. This allows the system to adapt to non-stationary conditions while maintaining computational feasibility through standardized statistical transformations.
Solution Approach 2:
The patent introduces anomaly scores as an intermediary metric between raw process data and outlier identification. These scores, computed based on Gaussian mixture models, serve as a bridge that enables precise anomaly detection in non-stationary systems without requiring direct complex statistical analysis of raw values.
2Measurement precision
If Gaussian mixture models are used to detect anomalies, then the anomaly detection precision is improved, but the computational complexity increases
Solution Approach 1:
The patent segments the complex GMM computation into distinct phases: offline model training using historical data, and online anomaly scoring using the trained model. This segmentation allows the computationally intensive parts to be performed once offline, while online operations use the pre-computed model for efficient real-time detection.
Solution Approach 2:
The patent performs preliminary actions by training the Gaussian mixture models offline using historical process data before actual anomaly detection begins. This preliminary model training captures the normal operating patterns, so that during online operation, only lightweight anomaly scoring is required, significantly reducing real-time computational complexity.
3Measurement precision
If anomaly scores are computed for all variables, then the detection accuracy is improved, but the processing time increases
Solution Approach 1:
The patent applies local quality by computing anomaly scores selectively for variables that are most relevant to the specific process context. Rather than uniformly processing all variables, the system can focus computational resources on critical variables where anomaly detection provides the most value, reducing overall processing time while maintaining detection accuracy for key parameters.
Data Source
AI summary
A method of improving at least one of quality and yield of a physical process comprises: obtaining values, from respective performances of the physical process, for a plurality of variables associated with the physical process; determining at least one Gaussian mixture model (GMM) representing the values for the variables for the performances of the physical process; based at least in part on the at least one GMM, computing at least one anomaly score for at least one of the variables for at least one of the performances of the physical process; based on the at least one anomaly score, identifying the at least one of the performances of the physical process as an outlier; and, based at least in part on the outlier identification, modifying the at least one of the variables for one or more subsequent performances of the physical process.