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

Chen, T, Morris, J and Martin, E (2006) Probability density estimation via an infinite Gaussian mixture model: application to statistical process monitoring J ROY STAT SOC C-APP, 55. 699 - 715. ISSN 0035-9254

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Abstract

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 infinity. 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.

Item Type: Article
Uncontrolled Keywords: Dirichlet process mixtures, infinite Gaussian mixture model, Markov chain Monte Carlo methods, multivariate statistical process monitoring, probability density estimation, PRINCIPAL COMPONENT ANALYSIS, BAYESIAN-ANALYSIS, UNKNOWN NUMBER
Divisions: Faculty of Engineering and Physical Sciences > Chemical and Process Engineering
Depositing User: Symplectic Elements
Date Deposited: 04 Aug 2011 14:06
Last Modified: 08 Nov 2013 12:08
URI: http://epubs.surrey.ac.uk/id/eprint/6482

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