Discriminant locality preserving projection chart for statistical monitoring of manufacturing processes

Abstract

In this paper, we propose a novel multivariate projection chart called the discriminant locality preserving projection chart. The basic idea of the chart is to seek an optimal linear projection of the original data including both the in-control reference data and the newly observed data for monitoring. The projection strives to not only preserve the locality structure of the original data but also maximise the separation between the in-control reference data and the newly observed data. With this projection, the low-dimensional projected data will then be monitored through a T² type of statistics. Comparing with the existing projection-based control chart, the proposed chart preserves the local data structure and adaptively identifies the best projection direction to detect the out-of-control data, and thus has more discriminating power, particularly for non-linearly related multidimensional data. The design issues of this chart are discussed in details in this paper. The effectiveness of the proposed method is verified by numerical studies and a real case study of forging process monitoring.

Keywords:

• statistical manufacturing process control
• multivariate process
• projection chart
• discriminant locality preserving projection

Acknowledgements

The authors would like to appreciate the anonymous reviewers for their valuable comments and suggestions.

Funding

Q. He is grateful for support from the National Natural Science Foundation of China under [grant number 51005221] and the Oversea Academic Training Funds–University of Science and Technology of China. S. Zhou is supported by the National Science Foundation of USA under [grant number 0856222].