Process Tracking and Analysis with L_x Exponential Smoothing from Noisy Measurements

References

• Barnard, G. (1959). Control charts and stochastic processes, Journal of the Royal Statistical Society — Series B, 21, 239–257.
   Google Scholar
• Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994). Time Series Analysis: Forecasting and Control, 3rd edition. Prentice-Hall, Englewood Cliffs, NJ.
   Google Scholar
• Brown, R. G. (1962). Smoothing, Forecasting and Prediction of Discrete Time Series. Prentice-Hall, Englewood Cliff, NJ.
   Google Scholar
• Chang, I., Tiao, G. C. and Chen C. (1988). Estimation of time series parameters in the presence of outliers. Technometrics, 30, 193–204.
   Google Scholar
• Chen, C. and Liu, L. M. (1993). Forecasting time series with outliers. Journal of Forecasting, 12, 13–35.
   Google Scholar
• Chen, A. and Elsayed, E. A. (2002). Design and performance analysis of the EWMA mean estimate for processes subject to random step changes. Technometrics, 44, 379–389.
   Google Scholar
• Chernoff, H. and Zacks, S. (1964). Estimating the current mean of a normal distribution which is subjected to changes in time. The Annals of Mathematical Statistics, 8, 83–97.
   Google Scholar
• Cipra, T. (1992). Robust exponential smoothing. Journal of Forecasting, 11, 57–69.
   Google Scholar
• Cox, D. R. (1961). Prediction by exponentially weighted moving average and related methods. Journal of Royal Statistical Society — Series B, 23, 414–442.
   Google Scholar
• Del Castillo, E. and Hurwitz, A. N. (1997). Run-to-run process control: A literature review and some extensions. Journal of Quality Technology, 29, 184–195.
   Google Scholar
• Deming, W. E. (2000). The New Economics for Industry, Government, Education, 2 nd edition. MIT Press.
   Google Scholar
• Donoho, D. L. and Huber, P. J. (1983). The notion of breakdown point. In A Festschrift for Erich L. Lehmann (eds P. J. Bickel, K. A. Doksum and J. L. Hodges, Jr), 157–184. Belmont: Wadsworth.
   Google Scholar
• Gardner, E. S. (1985). Exponential smoothing: The state of the art. Journal of Forecasting, 4, 1–28.
   Google Scholar
• Genton, M. G. and Lucas, A. (2003). Comprehensive definitions of breakdown points for independent and dependent observations, Journal of Royal Statistical Society—Series B, 65, 81–94.
   Google Scholar
• Hampel, F. R. (1971). A general qualitative definition of robustness. Annals of Mathematics Statistics, 42, 1887–1896.
   Google Scholar
• Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics— The Approach Based on Influence Functions. John Wiley & Sons, New York.
   Google Scholar
• Huber, P. J. (1981). Robust Statistics, John Wiley & Sons, New York.
   Google Scholar
• Hunter, J. S. (1986). The exponentially weighted moving average. Journal of Quality Technology, 18, 203–210.
   Google Scholar
• Ingolfsson, A. and Sachs, E. (1993). Statibility and sensitivity of an EWMA controller. Journal of Quality Technology, 25, 271–287.
   Google Scholar
• Jiang, W., Wu, H., Tsung, F., Nair, V. and Tsui K. L. (2002). Proportional integral derivative charts for process monitoring. Technometrics, 44 (3), 205–214.
   Google Scholar
• Jiang, W. and Zhu, Y. Z. (2009). Online process mean estimation using L x norm exponential smoothing. Naval Research Logistics, 56, 439–449.
   Google Scholar
• Liu, H., Shah, S. and Jiang, W. (2004). On-line outlier detection and data cleaning. Computers and Chemical Engineering, 28, 1635–1647.
   Google Scholar
• Luceno, A. (1998). Performance of discrete feedback adjustment schemes with dead band, under stationary versus nonstationary stochastic disturbance. Technometrics, 40, 223–233.
   Google Scholar
• Ma, Y. and Genton, M. G. (2000). Highly robust estimation of the autocovariance function. Journal of Time Series Analysis, 21, 663–684.
   Google Scholar
• Martin, R. D. and Thomson, D. J. (1982). Robust-resistant spectrum estimation. Proceeding of the IEEE, 70, 1097–1115.
   Google Scholar
• Martin, R. D. (1980). Robust estimation of autoregressive models. In Directions in Time Series, 228–262, Hayward: Institute of Mathematical Statistics.
   Google Scholar
• Martin, R. D. and Jong, J. M. (1977). Asymptotic Properties of Robust Generalized M-estimates for the First-order Autoregressive Parameter. Technical Memorandum, Bell Laboratories, Murray Hill.
   Google Scholar
• Montgomery, D. C. (2001). Introduction to Statistical Quality Control, 4th edition. Wiley, New York.
   Google Scholar
• Rousseeuw, P. J. and Leroy, A. M. (1987). Robust Regression and Outlier Detection, Wiley, New York.
   Google Scholar
• Tsay, R. S. (1988). Outliers, level shifts, and variance changes in time series. Journal of Forecasting, 7, 1–20.
   Google Scholar
• Tsung, F., Wu, H. and Nair, V. N. (1998). On efficiency and robustness of discrete proportional-integral control schemes. Technometrics, 40, 214–222.
   Google Scholar
• Yashchin, E. (1995). Estimating the current mean of a process subject to abrupt changes. Technometrics, 37, 311–323.
   Google Scholar