Journal of Intelligent Manufacturing

, Volume 27, Issue 4, pp 845–874 | Cite as

Simultaneous monitoring of mean vector and covariance matrix shifts in bivariate manufacturing processes using hybrid ensemble learning-based model



Many manufacturing processes are multivariate in nature because the quality of a given product is determined by several interrelated quality characteristics. Recently, various machine learning techniques (e.g., artificial neural network, support vector machine, support vector regression or decision tree) have been used as an effective tool to monitor process mean vector and covariance matrix shifts. However, most of these machine learning techniques-based approaches for process mean vector and covariance matrix have been developed separately in literature with the other parameter assumed to be under control. Little attention has been given to simultaneous monitoring of process mean vector and covariance matrix shifts. In addition, these approaches cannot provide more detailed shift information, for example the shift magnitude, which would be greatly useful for quality practitioners to search the assignable causes that give rise to the out-of-control situation. This study presents a hybrid ensemble learning-based model for simultaneous monitoring of process mean vector and covariance matrix shifts. The numerical results indicate that the proposed model can effectively detect and recognize not only mean vector or covariance matrix shifts but also mixed situations where mean vector and covariance matrix shifts exist concurrently. Meanwhile, the magnitude of the shift of each of the shifted quality characteristics can be accurately quantified. Empirical comparisons also show that the proposed model performs better than other existing approaches in detecting mean vector and covariance matrix shifts, while also providing the capability of recognition of shift types and quantification of shift magnitudes. A demonstrative example is provided.


Statistical process control Control charts Bivariate manufacturing processes Artificial neural network  Support vector machine Support vector regression 



The author would like to express their sincere thanks to the editor and the two anonymous reviewers for their detailed and helpful comments to improve the quality of this article.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mechanical and Electrical EngineeringNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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