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http://dx.doi.org/10.9709/JKSS.2011.20.4.067

Model Parameter Based Fault Detection for Time-series Data  

Park, Si-Jeo (고려대학교 산업경영공학과)
Park, Cheong-Sool (고려대학교 산업경영공학과)
Kim, Sung-Shick (고려대학교 산업경영공학과)
Baek, Jun-Geol (고려대학교 산업경영공학과)
Abstract
The statistical process control (SPC) assumes that observations follow the particular statistical distribution and they are independent to each other. However, the time-series data do not always follow the particular distribution, and most of cases are autocorrelated, therefore, it has limit to adopt the general SPC in tim series process. In this study, we propose a MPBC (Model Parameter Based Control-chart) method for fault detection in time-series processes. The MPBC builds up the process as a time-series model, and it can determine the faults by detecting changes parameters in the model. The process we analyze in the study assumes that the data follow the ARMA (p,q) model. The MPBC estimates model parameters using RLS (Recursive Least Square), and $K^2$-control chart is used for detecting out-of control process. The results of simulations support the idea that our proposed method performs better in time-series process.
Keywords
Time-series; Fault detection; Parameter monitoring; $K^2$-control chart; model-based; MPBC;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 김종락, 이언경, 김지선, 정민기, 박지영, 김창원(2004), "시계열 분석을 이용한 생물학적 수처리 공정의 거동 예측", 대한환경공학회 추계학술연구발표회 논문집, Vol. 10, pp. 925-928.
2 오창근, 나상섭, 이현구(1998), "비선형 ARMA 모델을 이용한 연속식 PS 중합 반응계의 식별", 한국화학공학회, Vol. 4, No. 2, pp. 2253.
3 이재헌, 김미정(2010), "자기회귀이동평균(1,1) 잡음모형에서 이상원인 탐지 및 재수정 절차", 한국데이터정보과학회지, Vol. 21, No. 5, pp. 841-852.
4 최인휴, 김정두(1994), "자기회귀-이동평균(ARMA) 모델에 의한 초음파 진동 절삭 공정의 해석", 한국정밀공학회지, Vol. 11, pp. 160-165.
5 Alessandri, A., Cuneo M., Pagnan S. and Sanguineti S. (2007), "A Recursive Algorithm for Nonlinear Leastsquares Problems", Computational Optimization Applications, Vol. 38, pp. 195-216.   DOI   ScienceOn
6 Anderson, T. W. and Darling, D. A. (1952), "Asymptotic theory of certain "goodness-of-fit" criteria based on stochastic processes". Annals of Mathematical Statistics, Vol. 23, pp. 193-212.   DOI   ScienceOn
7 Ann, Y. J. (2007), "Six Sigma and Quality Management", Parkyoungsa, Seoul, Korea.
8 Apley, D.W. and Tsung F. (2002), "The autoregressive T-squared chart for monitoring univariate autocorrelated processes", Journal of Quality Technology, Vol. 34, pp. 80-96.
9 Apley, D.W. (2002), "Time Series Control Charts in the Presence of Model Uncertainty", ASME Journal of Manufacturing Science and Engineering, Vol. 124, No. 4, pp. 891-898.   DOI   ScienceOn
10 Apley, D.W., and Shi, J. (1999), "GLRT for Statistical Process Control of Autocorrelated Processes", IIE Transactions, Vol. 31, No .12, pp. 1123-1134.
11 Bartkowiak, A.M. (2010), "Anomaly, novelty, one-class classification: A short introduction", Computer Information Systems and Industrial Management Applications (CISIM), 2010 International Conference on 8-10 Oct. 2010.
12 Bowerman, B., O'Connell R. and Koehler A. (2005), Forecasting Time Series and Regression, 4th Edition, Thomson Brooks.
13 Box, G.E.P., Jenkins G.M., and Reinsel G.C. (1994), Time Series Analysis: Forecasting and Control. Prentice- Hall, Inc.
14 Welch, G and Bishop, G. (2006), An Introduction to the Kalman Filter, http://www.cs.unc.edu/-welch, UNC-Chapel Hill, 95-041.
15 Goodwin, G.C. and Sin, K.S. (1984), Adaptive Filtering Prediction and Control. Prentice-Hall, Englewood Clifffs, N.J.
16 Harris, T. J. and Ross, W. H. (1991), "Statistical process control procedures for autocorrelated observations". The Canadian. Jounal of Chemical. Vol. 69, pp. 48-57.
17 Ljung, L. and Soderstrom, T. (1983), "Theory and Practice of Recursive Identification", The MIT Press, October 1983, pp. 551
18 Healy J.D. (1987), "A note on multivariate CUSUM procedure". Technometrics Vol. 29, pp. 409-412.   DOI   ScienceOn
19 Hu, S. J. and Roan, C. (1996), "Change patterns of time series-based control charts". Journal of Quality Technology, Vol. 28, pp. 302-312.
20 Kim, S. B., Weerawat, J. and Thuntee, S. (2010), "One- Class Classification-Based Control Chart for Monitoring Autocorrelated Multivariate Processes" Communications in Statistics-Simulation and Computation, Vol. 39, pp. 461-474.   DOI   ScienceOn
21 Lu, C. W. and Reynolds, M. R. (1999a), "Control chart for monitoring the mean and variance of autocorrelated processes". Journal of Quality Technology. Vol. 31, pp. 259-274.
22 Massey, F. J. (1951), "The Kolmogorov-Smirnov Test for Goodness of Fit". Journal of the American Statistical Association. Vol. 46, pp. 68-78.   DOI   ScienceOn
23 Mandel, B.J. (1969), "The regression control chart". Journal of Quality Technology. Vol. 1, pp. 1-9.
24 Montgomery, D. C. (2001), Introduction to Statistical Quality Control, 5th Edition, Hohn Wiley & Sons, NewYork, NY, 2001.
25 Tax, D.M.J. (2001), One-Class Classification: Concept- Learning in the Absence of Counter-Examples, PhD thesis, Delf University of Technology, Netherlands.
26 Moonen, M. (2004), Introduction to adaptive signal processing, Department of Electronic Engineering, Belgium; ALARI/DSP - Lecture 4.
27 Pandit, S. M. and Wu, S. (1983), Time Series and System Analysis with Application, John Wiley, New York. pp. 291, 491-492.
28 Sukchotrat, T., Kim, S.B. and Tsung, F. (2010), "Oneclass Classification-based control charts for Multivariate process monitoring". IIE Transactions. Vol. 42, No. 2, pp. 107-120.
29 Tsung, F. and Tsui, K. L. (2003), "A mean-shift pattern study on integration of SPC and APC for process monitoring". IIE Transactions, Vol. 35, pp. 231-242.   DOI   ScienceOn