Wavelet-Based Profile Monitoring Using Order-Thresholding Recursive CUSUM Schemes

  • Ruizhi ZhangEmail author
  • Yajun Mei
  • Jianjun Shi
Part of the ICSA Book Series in Statistics book series (ICSABSS)


With the rapid development of advanced sensing technologies, rich and complex real-time profile or curve data are available in many processes in biomedical sciences and manufacturing. These profile data provide valuable intrinsic information about the performance or properties of the process, subject, or product, and it is often desirable to utilize them to develop efficient methodologies for process monitoring and fault diagnosing. In this article, we propose a novel wavelet-based profile monitoring procedure that is based on the order-thresholding transformation of recursive CUSUM statistics of multiple wavelet coefficients. Extensive simulation studies and a case study of tonnage profile data demonstrate that our proposed procedure is efficient for detecting the unknown local changes on the profile.



This research is partially supported by NSF grant CMMI-1362876.


  1. Chang, S. I., & Yadama, S. (2010). Statistical process control for monitoring non-linear profiles using wavelet filtering and b-spline approximation. International Journal of Production Research, 48(4), 1049–1068.CrossRefGoogle Scholar
  2. Chang, T. C., & Gan, F. F. (2006). Monitoring linearity of measurement gauges. Journal of Statistical Computation and Simulation, 76(10), 889–911.MathSciNetCrossRefGoogle Scholar
  3. Chen, S., & Nembhard, H. B. (2011). A high-dimensional control chart for profile monitoring. Quality and Reliability Engineering International, 27(4), 451–464.CrossRefGoogle Scholar
  4. Chicken, E., Pignatiello, J. J., Jr., & Simpson, J. R. (2009). Statistical process monitoring of nonlinear profiles using wavelets. Journal of Quality Technology, 41(2), 198.CrossRefGoogle Scholar
  5. Daubechies, I. (1992). Ten lectures on wavelets. Philadelphia: SIAM.CrossRefGoogle Scholar
  6. Donoho, D. L., & Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81(3), 425–455.MathSciNetCrossRefGoogle Scholar
  7. Donoho, D. L., & Johnstone, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association, 90(432), 1200–1224.MathSciNetCrossRefGoogle Scholar
  8. Donoho, D. L., & Johnstone, I. M. (1998). Minimax estimation via wavelet shrinkage. The Annals of Statistics, 26(3), 879–921.MathSciNetCrossRefGoogle Scholar
  9. Fan, J. (1996). Test of significance based on wavelet thresholding and Neyman’s truncation. Journal of the American Statistical Association, 91(434), 674–688.MathSciNetCrossRefGoogle Scholar
  10. Fan, J., & Lin, S. K. (1998). Test of significance when data are curves. Journal of the American Statistical Association, 93(443), 1007–1021.MathSciNetCrossRefGoogle Scholar
  11. Gardner, M. M., Lu, J. C., Gyurcsik, R. S., Wortman, J. J., Hornung, B. E., Heinisch, H. H., et al. (1997). Equipment fault detection using spatial signatures. IEEE Transactions on Components, Packaging, and Manufacturing Technology: Part C, 20(4), 295–304.CrossRefGoogle Scholar
  12. Hall, P., Poskitt, D. S., & Presnell, B. (2001). A functional data-analytic approach to signal discrimination. Technometrics, 43(1), 1–9.MathSciNetCrossRefGoogle Scholar
  13. James, W., & Stein, C. (1961). Estimation with quadratic loss. In Proceedings of the fourth Berkeley symposium on mathematical statistics and probability (vol. 1, pp. 361–379).Google Scholar
  14. Jeong, M. K., Lu, J. C., & Wang, N. (2006). Wavelet-based SPC procedure for complicated functional data. International Journal of Production Research, 44(4), 729–744.CrossRefGoogle Scholar
  15. Jin, J., & Shi, J. (1999). Feature-preserving data compression of stamping tonnage information using wavelets. Technometrics, 41(4), 327–339.CrossRefGoogle Scholar
  16. Jin, J., & Shi, J. (2001). Automatic feature extraction of waveform signals for in-process diagnostic performance improvement. Journal of Intelligent Manufacturing, 12(3), 257–268.CrossRefGoogle Scholar
  17. Kang, L., & Albin, S. L. (2000). On-line monitoring when the process yields a linear profile. Journal of Quality Technology, 32(4), 418.CrossRefGoogle Scholar
  18. Kazemzadeh, R. B., Noorossana, R., & Amiri, A. (2008). Phase I monitoring of polynomial profiles. Communications in Statistics–Theory and Methods, 37(10), 1671–1686.MathSciNetCrossRefGoogle Scholar
  19. Kim, M. H., & Akritas, M. G. (2010). Order thresholding. The Annals of Statistics 38(4), 2314–2350.MathSciNetCrossRefGoogle Scholar
  20. Lee, J., Hur, Y., Kim, S. H., & Wilson, J. R. (2012). Monitoring nonlinear profiles using a wavelet-based distribution-free CUSUM chart. International Journal of Production Research, 50(22), 6574–6594.CrossRefGoogle Scholar
  21. Lei, Y., Zhang, Z., & Jin, J. (2010). Automatic tonnage monitoring for missing part detection in multi-operation forging processes. Journal of Manufacturing Science and Engineering, 132(5), 051010.CrossRefGoogle Scholar
  22. Liu, K., Zhang, R., & Mei, Y. (2017). Scalable sum-shrinkage schemes for distributed monitoring large-scale data streams. Statistica Sinica (Accepted).Google Scholar
  23. Lorden, G. (1971). Procedures for reacting to a change in distribution. The Annals of Mathematical Statistics, 42(6), 1897–1908.MathSciNetCrossRefGoogle Scholar
  24. Lorden, G., & Pollak, M. (2008). Sequential change-point detection procedures that are nearly optimal and computationally simple. Sequential Analysis, 27(4), 476–512.MathSciNetCrossRefGoogle Scholar
  25. Mallat, S. (1999). A wavelet tour of signal processing. London: Academic Press.zbMATHGoogle Scholar
  26. Mallat, S. G. (1989). Multifrequency channel decompositions of images and wavelet models. IEEE Transactions on Acoustics, Speech, and Signal Processing 37(12), 2091–2110.CrossRefGoogle Scholar
  27. Moustakides, G. V. (1986). Optimal stopping times for detecting changes in distributions. The Annals of Statistics, 14(4), 1379–1387.MathSciNetCrossRefGoogle Scholar
  28. Neyman, J. (1937). Smooth test for goodness of fit. Scandinavian Actuarial Journal, 20(3–4), 149–199.CrossRefGoogle Scholar
  29. Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1–2), 100–115.MathSciNetCrossRefGoogle Scholar
  30. Paynabar, K., Zou, C., & Qiu, P. (2016). A change-point approach for phase-i analysis in multivariate profile monitoring and diagnosis. Technometrics, 58(2), 191–204.MathSciNetCrossRefGoogle Scholar
  31. Qiu, P., Zou, C., & Wang, Z. (2010). Nonparametric profile monitoring by mixed effects modeling. Technometrics, 52(3), 265–277.MathSciNetCrossRefGoogle Scholar
  32. Zhou, C., Liu, K., Zhang, X., Zhang, W., & Shi, J. (2016). An automatic process monitoring method using recurrence plot in progressive stamping processes. IEEE Transactions on Automation Science and Engineering, 13(2), 1102–1111.CrossRefGoogle Scholar
  33. Zhou, S., Sun, B., & Shi, J. (2006). An SPC monitoring system for cycle-based waveform signals using Haar transform. IEEE Transactions on Automation Science and Engineering, 3(1), 60–72.CrossRefGoogle Scholar
  34. Zou, C., & Qiu, P. (2009). Multivariate statistical process control using lasso. Journal of the American Statistical Association, 104(488), 1586–1596.MathSciNetCrossRefGoogle Scholar
  35. Zou, C., Qiu, P., & Hawkins, D. (2009). Nonparametric control chart for monitoring profiles using change point formulation and adaptive smoothing. Statistica Sinica, 19(3), 1337–1357.MathSciNetzbMATHGoogle Scholar
  36. Zou, C., Tsung, F., & Wang, Z. (2007). Monitoring general linear profiles using multivariate exponentially weighted moving average schemes. Technometrics, 49(4), 395–408.MathSciNetCrossRefGoogle Scholar
  37. Zou, C., Wang, Z., Zi, X., & Jiang, W. (2015). An efficient online monitoring method for high-dimensional data streams. Technometrics, 57(3), 374–387.MathSciNetCrossRefGoogle Scholar
  38. Zou, C., Zhou, C., Wang, Z., & Tsung, F. (2007). A self-starting control chart for linear profiles. Journal of Quality Technology, 39(4), 364–375.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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