Maximum Covariance Unfolding Regression: A Novel Covariate-based Manifold Learning Approach for Point Cloud Data

Point cloud data are widely used in manufacturing applications for process inspection, modeling, monitoring and optimization. The state-of-art tensor regression techniques have effectively been used for analysis of structured point cloud data, where the measurements on a uniform grid can be formed into a tensor. However, these techniques are not capable of handling unstructured point cloud data that are often in the form of manifolds. In this paper, we propose a nonlinear dimension reduction approach named Maximum Covariance Unfolding Regression that is able to learn the low-dimensional (LD) manifold of point clouds with the highest correlation with explanatory covariates. This LD manifold is then used for regression modeling and process optimization based on process variables. The performance of the proposed method is subsequently evaluated and compared with benchmark methods through simulations and a case study of steel bracket manufacturing

Identifying the period of a step change in high-yield processes

Quality control charts have proven to be very effective in detecting out-of-control states. When a signal is detected a search begins to identify and eliminate the source(s) of the signal. A critical issue that keeps the mind of the process engineer busy at this point is determining the time when the process first changed. Knowing when the process first changed can assist process engineers to focus efforts effectively on eliminating the source(s) of the signal. The time when a change in the process takes place is referred to as the change point. This paper provides an estimator for a period of time in which a step change in the process non-conformity proportion in high-yield processes occurs. In such processes, the number of items until the occurrence of the first non-conforming item can be modeled by a geometric distribution. The performance of the proposed model is investigated through several numerical examples. The results indicate that the proposed estimator provides a reasonable estimate for the period when the step change occurred at the process non-conformity level. Copyright © 2009 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/64306/1/1007_ftp.pd