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Probability density estimation via an infinite Gaussian mixture model: Application to statistical process monitoring

Lookup NU author(s): Dr Tao Chen, Emeritus Professor Julian Morris, Professor Elaine Martin


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The primary goal of multivariate statistical process performance monitoring is to identify deviations from normal operation within a manufacturing process. The basis of the monitoring schemes is historical data that have been collected when the process is running under normal operating conditions. These data are then used to establish confidence bounds to detect the onset of process deviations. In contrast with the traditional approaches that are based on the Gaussian assumption, this paper proposes the application of the infinite Gaussian mixture model (GMM) for the calculation of the confidence bounds, thereby relaxing the previous restrictive assumption. The infinite GMM is a special case of Dirichlet process mixtures and is introduced as the limit of the finite GMM, i.e. when the number of mixtures tends to ∞. On the basis of the estimation of the probability density function, via the infinite GMM, the confidence bounds are calculated by using the bootstrap algorithm. The methodology proposed is demonstrated through its application to a simulated continuous chemical process, and a batch semiconductor manufacturing process. © 2006 Royal Statistical Society.

Publication metadata

Author(s): Chen T, Morris J, Martin E

Publication type: Article

Publication status: Published

Journal: Journal of the Royal Statistical Society. Series C: Applied Statistics

Year: 2006

Volume: 55

Issue: 5

Pages: 699-715

ISSN (print): 0035-9254

ISSN (electronic): 1467-9876

Publisher: Wiley-Blackwell Publishing Ltd.


DOI: 10.1111/j.1467-9876.2006.00560.x


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