A new multivariate control chart based on the isolation forest algorithm

Abstract

Statistical process control (SPC) is an extensively utilized technique in quality management for service and manufacturing industries. Traditional SPC control charts rely on normality assumptions and analyze data in one dimension. Machine learning methods have been increasingly used to address limitations of traditional SPC techniques, such as one-class classification (OCC) procedures, using support vector machine (SVM), K-nearest neighbor (KNN), and other techniques. Nonetheless, there are drawbacks associated with these methods. For instance, SVM-based approaches may require significant computational resources, whereas KNN-based approaches may encounter difficulties in identifying minor variations. Here, these limitations are addressed using a new SPC framework that incorporates the isolation forest (iForest) algorithm, an unsupervised anomaly detection technique developed for machine learning applications. Our presented method examines how the number of trees impacts the charting scheme and offers several advantages: (1) it has a low constant time complexity that results in fast computing speeds; (2) it outperforms competitors in detecting small shifts in various distributions; and (3) while dealing with challenging distributions with heavy tails, it proves to be effective. We provide two examples that demonstrate the performance of our proposed control chart using Monte Carlo simulations.

Keywords:

• EWMA
• multivariate process
• isolation tree
• support vector machine
• K-nearest neighbor

Acknowledgements

The authors express their sincere thanks to the editors and reviewers for their most valuable comments and suggestions in improving this paper greatly.

Disclosure statement

The authors declare no potential conflicts of interest.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China, and the funding number is 12075162.

Notes on contributors

Jing Wang

Jing Wang is a doctoral student at the School of Mathematical Sciences, Sichuan Normal University. Her research interests include machine learning and statistical process control.

Liu Liu

Liu Liu is the dean of the College of Mathematics and Physics at Chengdu University of Technology. He is a professor and a doctoral supervisor. He obtained his PhD degree in Mathematics from Sichuan Normal University and his research interests include big data analysis, statistical process control, and medical statistics.