WorkshopsDistribution-Free Profile Monitoring Schemes
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Nonparametric or distribution-free methodologies have become important tools in statistical process control because the underlying distribution of process data is often unavailable in real applications. Different from the traditional production processes where the quality characteristics are measured as univariate or multivariate variables, numerous modern industrial processes are interested in the functional relationship between the response and covariate(s) variables, or so-called profile in the literature. In this study, we propose new distribution-free control charts for profile data for Phase I and II analyses. By applying principal component analysis to the variance-covariance matrix of smoothed (discretized) profiles, the eigenvector- value pairs and the corresponding principal component (PC) scores can be calculated. The PC scores are then separated into two groups. The first group elucidates the majority of the total variation, and the second group represents errors in the data. Two Hotelling T2 statistics are used to monitor changes in the two spaces spanned by the two groups of the PC scores, respectively. By using the distribution-free multivariate monitoring schemes for the random vector composed of the two T2 statistics, distribution-free control charts can be constructed for the profiles. Distribution- free methods based on spatial signs are considered in our proposal. Simulation results show that our methods are effective in detecting changes in the location and the scatter matrix of the process distribution. Actual data from a semiconductor manufacturing procedure are used to demonstrate the proposed method.
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Jyh-Jen Horng
2012-12-21
15:40:00 - 16:30:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
Nonparametric or distribution-free methodologies have become important tools in statistical process control because the underlying distribution of process data is often unavailable in real applications. Different from the traditional production processes where the quality characteristics are measured as univariate or multivariate variables, numerous modern industrial processes are interested in the functional relationship between the response and covariate(s) variables, or so-called profile in the literature. In this study, we propose new distribution-free control charts for profile data for Phase I and II analyses. By applying principal component analysis to the variance-covariance matrix of smoothed (discretized) profiles, the eigenvector- value pairs and the corresponding principal component (PC) scores can be calculated. The PC scores are then separated into two groups. The first group elucidates the majority of the total variation, and the second group represents errors in the data. Two Hotelling T2 statistics are used to monitor changes in the two spaces spanned by the two groups of the PC scores, respectively. By using the distribution-free multivariate monitoring schemes for the random vector composed of the two T2 statistics, distribution-free control charts can be constructed for the profiles. Distribution- free methods based on spatial signs are considered in our proposal. Simulation results show that our methods are effective in detecting changes in the location and the scatter matrix of the process distribution. Actual data from a semiconductor manufacturing procedure are used to demonstrate the proposed method.