A Vertical-Energy-Thresholding Procedure for Data Reduction With Multiple Complex Curves

Due to the development of sensing and computer technology, measurements of many process variables are available in current manufacturing processes. It is very challenging, however, to process a large amount of information in a limited time in order to make decisions about the health of the processes and products. This paper develops a “preprocessing” procedure for multiple sets of complicated functional data in order to reduce the data size for supporting timely decision analyses. The data type studied has been used for fault detection, root-cause analysis, and quality improvement in such engineering applications as automobile and semiconductor manufacturing and nanomachining processes. The proposed vertical-energy-thresholding (VET) procedure balances the reconstruction error against data-reduction efficiency so that it is effective in capturing key patterns in the multiple data signals. The selected wavelet coefficients are treated as the “reduced-size” data in subsequent analyses for decision making. This enhances the ability of the existing statistical and machine-learning procedures to handle high-dimensional functional data. A few real-life examples demonstrate the effectiveness of our proposed procedure compared to several ad hoc techniques extended from single-curve-based data modeling and denoising procedures.