MULTIVARIATE CUSUM CONTROL CHART BASED ON THE RESIDUALS OF MULTIOUTPUT LEAST SQUARES SVR FOR MONITORING WATER QUALITY
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Published:
Sep 30, 2019
Keywords:
autocorrelated control chart multioutput least squares SVR multivariate CUSUM water quality
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Abstract
Monitoring serially dependent processes using conventional control charts yields a high false alarm rate. Multioutput Least Squares Support Vector Regression (MLS-SVR) has the capability to encompass the cross-relatedness between output variables by learning multivariate output variables simultaneously. This research aims to develop a Multivariate Cumulative Sum (MCUSUM) control chart based on the residual obtained from the MLS-SVR model for monitoring autocorrelated data. The inputs of the MLS-SVR are selected using the significant lag of a partial autocorrelation function. The proposed control chart is applied to monitor water quality data and it can detect the assignable causes in those data caused by a broken pipeline.
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Khusna, H., Mashuri, M., S., S., Prastyo, D. D., & Ahsan, M. (2019). MULTIVARIATE CUSUM CONTROL CHART BASED ON THE RESIDUALS OF MULTIOUTPUT LEAST SQUARES SVR FOR MONITORING WATER QUALITY. Malaysian Journal of Science, 38(Sp2), 73–83. https://doi.org/10.22452/mjs.sp2019no2.7
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ISMI-ICTAS18 (Published)
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References
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Chan L K., and Li G-Y. (1994). A multivariate control chart for detecting linear trends, Communications in Statistics-Simulation and Computation 23 (4):997–1012.
Charnes J M. (1995). Tests for special causes with multivariate autocorrelated data, Computers and Operations Research 22 (4):443–453.
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Härdle W K., Prastyo D D., and Hafner C M. (2014). Support vector machines with evolutionary model selection for default prediction. The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics. Oxford University Press.
Harris T J., and Ross W H. (1991). Statistical process control procedures for correlated observations, Canadian Journal of Chemical Engineering 69 (1):48–57.
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Issam B K., and Mohamed L. (2008). Support vector regression based residual MCUSUM control chart for autocorrelated process, Applied Mathematics and Computation 201 (1–2):565–574.
Johnson R A., and Bagshaw M. (1974). The effect of serial correlation on the performance of CUSUM tests, Technometrics 16 (1):103–112.
Kalgonda A A., and Kulkarni S R. (2004). Multivariate quality control chart for autocorrelated processes, Journal of Applied Statistics 31 (3):317–327.
Khediri I B., Weihs C., and Limam M. (2010). Support vector regression control charts for multivariate nonlinear autocorrelated processes, Chemometrics and Intelligent Laboratory Systems 103 (1):76–81.
Khusna H., Mashuri M., Prastyo D D., and Ahsan M. (2018). Multioutput least square SVR based multivariate EWMA control chart, Journal of Physics: Conference Series 1028:12221. IOP Publishing.
Kramer H G., and Schmid L V. (1997). EWMA charts for multivariate time series, Sequential Analysis 16 (2):131–154.
Liu G., Lin Z., and Yu Y. (2009). Multi-output regression on the output manifold, Pattern Recognition 42 (11):2737–2743.
Lowry C A., Woodall W H., Champ C W., and Rigdon S E. (1992). A multivariate exponentially weighted moving average control chart, Technometrics 34 (1):46–53.
Ngai H-M., and Zhang J. (2001). Multivariate cumulative sum control charts based on projection pursuit, Statistica Sinica 747–766.
Noorossana R., and Vaghefi S J M. (2006). Effect of autocorrelation on performance of the MCUSUM control chart, Quality and Reliability Engineering International 22 (2), 191–197.
Pignatiello J J., and Runger G C. (1990). Comparisons of multivariate CUSUM charts, Journal of Quality Technology 22 (3):173–186.
Psarakis S., and Papaleonida G. (2007). SPC procedures for monitoring autocorrelated processes, Quality Technology and Quantitative Management 4 (4):501–540.
Sato J R., Costafreda S., Morettin P A., and Brammer M J. (2008). Measuring time series predictability using support vector regression, Communications in Statistics-Simulation and Computation 37 (6):1183–1197.
Śliwa P., and Schmid W. (2005). Monitoring the cross-covariances of a multivariate time series, Metrika 61 (1):89–115.
Suykens J A K., Van-Gestel T., De-Brabanter J., De-Moor B., and Vandewalle J. (2002). Least squares support vector machines. World Scientific.
Suykens J A K., and Vandewalle J. (1999). Multiclass least squares support vector machines, IEEE 2:900-903.
Theodossiou P. (1993). Predicting shifts in the mean of a multivariate time series process: an application in predicting business failures, Journal of the American Statistical Association 88:441–449.
Thissen U., Van-Brakel R., De-Weijer A P., Melssen W J., and Buydens L M C. (2003). Using support vector machines for time series prediction, Chemometrics and Intelligent Laboratory Systems 69 (1–2):35–49.
Tuia D., Verrelst J., Alonso L., Perez-Cruz F., and Camps-Valls G. (2011). Multioutput support vector regression for remote sensing biophysical parameter estimation, IEEE Geoscience and Remote Sensing Letters 8 (4):804–808.
Vanbrackle L N., and Reynolds M R. (1997). EWMA and CUSUM control charts in the presence of correlation, Communications in Statistics-Simulation and Computation 26 (3):979–1008.
Vapnik V N. (1998). Statistical Learning Theory. John Wiley & Sons.
Vapnik V N. (2000). The Nature of Statistical Learning Theory 8.
Woodall W H., and Montgomery D C. (1999). Research issues and ideas in statistical process control, Journal of Quality Technology 31 (4):11.
Wororomi J K., Mashuri M., Irhamah, and Arifin A Z. (2014). On monitoring shift in the mean processes with vector autoregressive residual control charts of individual observation, Applied Mathematical Sciences 8:3491–3499.
Xu S., An X., Qiao X., Zhu L., and Li, L. (2013). Multi-output least-squares support vector regression machines, Pattern Recognition Letters 34 (9):1078–1084.
Yashchin E. (1993). Performance of CUSUM control schemes for serially correlated observations. Technometrics 35 (1):37–52.
Chan L K., and Li G-Y. (1994). A multivariate control chart for detecting linear trends, Communications in Statistics-Simulation and Computation 23 (4):997–1012.
Charnes J M. (1995). Tests for special causes with multivariate autocorrelated data, Computers and Operations Research 22 (4):443–453.
Crosier R B. (1988). Multivariate generalizations of cumulative sum quality-control schemes, Technometrics 30 (3):291–303.
Härdle W K., Prastyo D D., and Hafner C M. (2014). Support vector machines with evolutionary model selection for default prediction. The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics. Oxford University Press.
Harris T J., and Ross W H. (1991). Statistical process control procedures for correlated observations, Canadian Journal of Chemical Engineering 69 (1):48–57.
Healy J D. (1987). A note on multivariate CUSUM procedures, Technometrics 29 (4):409–412.
Hsu C W., Chang C C., and Lin C J. (2016). A practical guide to support vector classification. National Taiwan University.
Hwang C. (2016). Multioutput LS-SVR based residual MCUSUM control chart for autocorrelated process, Journal of the Korean Data and Information Science Society 27 (2):523–530.
Issam B K., and Mohamed L. (2008). Support vector regression based residual MCUSUM control chart for autocorrelated process, Applied Mathematics and Computation 201 (1–2):565–574.
Johnson R A., and Bagshaw M. (1974). The effect of serial correlation on the performance of CUSUM tests, Technometrics 16 (1):103–112.
Kalgonda A A., and Kulkarni S R. (2004). Multivariate quality control chart for autocorrelated processes, Journal of Applied Statistics 31 (3):317–327.
Khediri I B., Weihs C., and Limam M. (2010). Support vector regression control charts for multivariate nonlinear autocorrelated processes, Chemometrics and Intelligent Laboratory Systems 103 (1):76–81.
Khusna H., Mashuri M., Prastyo D D., and Ahsan M. (2018). Multioutput least square SVR based multivariate EWMA control chart, Journal of Physics: Conference Series 1028:12221. IOP Publishing.
Kramer H G., and Schmid L V. (1997). EWMA charts for multivariate time series, Sequential Analysis 16 (2):131–154.
Liu G., Lin Z., and Yu Y. (2009). Multi-output regression on the output manifold, Pattern Recognition 42 (11):2737–2743.
Lowry C A., Woodall W H., Champ C W., and Rigdon S E. (1992). A multivariate exponentially weighted moving average control chart, Technometrics 34 (1):46–53.
Ngai H-M., and Zhang J. (2001). Multivariate cumulative sum control charts based on projection pursuit, Statistica Sinica 747–766.
Noorossana R., and Vaghefi S J M. (2006). Effect of autocorrelation on performance of the MCUSUM control chart, Quality and Reliability Engineering International 22 (2), 191–197.
Pignatiello J J., and Runger G C. (1990). Comparisons of multivariate CUSUM charts, Journal of Quality Technology 22 (3):173–186.
Psarakis S., and Papaleonida G. (2007). SPC procedures for monitoring autocorrelated processes, Quality Technology and Quantitative Management 4 (4):501–540.
Sato J R., Costafreda S., Morettin P A., and Brammer M J. (2008). Measuring time series predictability using support vector regression, Communications in Statistics-Simulation and Computation 37 (6):1183–1197.
Śliwa P., and Schmid W. (2005). Monitoring the cross-covariances of a multivariate time series, Metrika 61 (1):89–115.
Suykens J A K., Van-Gestel T., De-Brabanter J., De-Moor B., and Vandewalle J. (2002). Least squares support vector machines. World Scientific.
Suykens J A K., and Vandewalle J. (1999). Multiclass least squares support vector machines, IEEE 2:900-903.
Theodossiou P. (1993). Predicting shifts in the mean of a multivariate time series process: an application in predicting business failures, Journal of the American Statistical Association 88:441–449.
Thissen U., Van-Brakel R., De-Weijer A P., Melssen W J., and Buydens L M C. (2003). Using support vector machines for time series prediction, Chemometrics and Intelligent Laboratory Systems 69 (1–2):35–49.
Tuia D., Verrelst J., Alonso L., Perez-Cruz F., and Camps-Valls G. (2011). Multioutput support vector regression for remote sensing biophysical parameter estimation, IEEE Geoscience and Remote Sensing Letters 8 (4):804–808.
Vanbrackle L N., and Reynolds M R. (1997). EWMA and CUSUM control charts in the presence of correlation, Communications in Statistics-Simulation and Computation 26 (3):979–1008.
Vapnik V N. (1998). Statistical Learning Theory. John Wiley & Sons.
Vapnik V N. (2000). The Nature of Statistical Learning Theory 8.
Woodall W H., and Montgomery D C. (1999). Research issues and ideas in statistical process control, Journal of Quality Technology 31 (4):11.
Wororomi J K., Mashuri M., Irhamah, and Arifin A Z. (2014). On monitoring shift in the mean processes with vector autoregressive residual control charts of individual observation, Applied Mathematical Sciences 8:3491–3499.
Xu S., An X., Qiao X., Zhu L., and Li, L. (2013). Multi-output least-squares support vector regression machines, Pattern Recognition Letters 34 (9):1078–1084.
Yashchin E. (1993). Performance of CUSUM control schemes for serially correlated observations. Technometrics 35 (1):37–52.