Phase I analysis for monitoring nonlinear profiles in manufacturing processes
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Phase I analysis of nonlinear profiles aims at identifying the data from an in-control process as accurately as possible so that quality engineers can have a good reference to establish the control charts for a future process. Unlike linear profiles, which can be represented by a linear regression model with its model parameters used for monitoring and detection, nonlinear profiles are often sampled into high-dimensional data vectors and analyzed by nonparametric methods. Meanwhile, automatic in-process data-collection devices generate huge historical data sets, which must be analyzed for the presence of observations from out-of-control process conditions. The high dimensionality and data contamination present a challenge to the Phase I analysis of nonlinear profiles. This paper presents a strategy that consists of two major components: a data-reduction component that projects the original data into a lower dimension subspace while preserving the data-clustering structure and a data-separation technique that can detect single and multiple shifts as well as outliers in the data. Simulated data sets as well as nonlinear profile signals from a forging process are used to illustrate the effectiveness of the proposed strategy.