Wavelet-Based Data Reduction Techniques for Process Fault Detection

• Published in: Technometrics Vol. 48; no. 1; pp. 26 - 40
• Main Authors: Jeong, Myong K, Lu, Jye-Chyi, Huo, Xiaoming, Vidakovic, Brani, Di Chen
• Format: Journal Article
• Language: English
• Published: Alexandria, VI Taylor & Francis 01.02.2006; Milwaukee, WI The American Society for Quality and The American Statistical Association; American Society for Quality Control; American Statistical Association; American Society for Quality
• Subjects: Antennas; Applied sciences; Approximation; Attitude scales; Carts; Computer science; control theory; systems; Data acquisition systems; Data compression; Data denoising; Data mining; Data processing. List processing. Character string processing; Data reduction; Datasets; Exact sciences and technology; Information retrieval noise; Mathematics; Memory organisation. Data processing; Methods; Probability and statistics; Quality; Quality improvement; Scalogram; Sciences and techniques of general use; Signal noise; Signal processing; Software; Statistics; Supernova remnants; Threshing; Wavelet transforms; Data analysis; Wavelet transformation; Decision making; Noise reduction; Signal processing; Data mining; Data reduction; Defect detection
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/004017005000000553

This article presents new data reduction methods based on the discrete wavelet transform to handle potentially large and complicated nonstationary data curves. The methods minimize objective functions to balance the trade-off between data reduction and modeling accuracy. Theoretic investigations provide the optimality of the methods and the large-sample distribution of a closed-form estimate of the thresholding parameter. An upper bound of errors in signal approximation (or estimation) is derived. Based on evaluation studies with popular testing curves and real-life datasets, the proposed methods demonstrate their competitiveness with the existing engineering data compression and statistical data denoising methods for achieving the data reduction goals. Further experimentation with a tree-based classification procedure for identifying process fault classes illustrates the potential of the data reduction tools. Extension of the engineering scalogram to the reduced-size semiconductor fabrication data leads to a visualization tool for monitoring and understanding process problems.