Probability Density Estimation via Infinite Gaussian Mixture Model: Application to Statistical Process Monitoring
نویسندگان
چکیده
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 has been collected when the process is running under normal operating conditions. This data is then used to establish confidence bounds to detect the onset of process deviations. In contrast to 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, that is when the number of mixtures tends to infinity. Based on the estimation of the probability density function, via the infinite GMM, the confidence bounds are calculated using the bootstrap algorithm. The proposed methodology is demonstrated through its application to a simulated continuous chemical process, and a batch semiconductor manufacturing process.
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