Monitoring process mean using a second-order filter: Signal and system approach

Document Type : Article


Department of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran


In statistical process control one objective is to control the stability of a process. A process is stable when its mean is in control and variance bounded. Different control charts were introduced for monitoring the mean and variance of a process by plotting suitable test statistics on the chart. In this research design of a system which converts the sample mean to a test statistics was proposed. The second order filter, a special class of the Linear Time Invariant (LTI) systems, was used to design the converting system. It was shown that design of a low pass filter was better for detecting a level (mean) change in the process. Markov chain approach was also followed to construct appropriate control chart and to estimate its control limits. Simulated data under normality assumption for different scenarios were used to compare the proposed control chart with Shewhart and Exponentially Weighted Moving Average charts by means of ARL and PFS criteria. Existing data from the Central Bank of Iran was also applied to evaluate the suggested method. The signal to noise ratio was used to assess the performance of this method at different stages. Results indicate that the proposed method detects shifts more rapidly.


1. Montgomery, D.C., Introduction to Statistical Quality Control, John Wiley and Sons, New York (2013).
2. Jiang, W. "Average run length computation of ARMA charts for stationary processes", Communications in Statistics-Simulation and Computation, 30(3), pp. 699-716 (2007).
3. Wu, Z. and Spedding, T.A. "A synthetic control chart for detecting small shifts in the process mean", Journal of Quality Technology, 32(1), pp. 32-38 (2000).
4. Zhang, N.F. "A statistical control chart for stationary process data", Technometrics, 40(1), pp. 24-38 (1998).
5. Chang, S.I. and Aw, C.A. "A neural fuzzy control chart for detecting and classifying process mean shifts", International Journal of Production Research, 34(8), pp. 2265-2278 (1996).
6. Harris, T.J. and Ross, W.H. "Statistical process control procedures for correlated observations", The Canadian Journal of Chemical Engineering, 69, pp. 48-57 (1991).
7. Saif, A.W. "A frame work for the integration of statistical process control and engineering process control", Industrial & Systems Engineering Conference (ISEC), Jeddah, Saudi Arabia (2019).
8. Rabyk, L. and Schmid, W. "EWMA control charts for detecting changes in the mean of a long-memory process", Metrika, 79(3), pp. 267-301 (2016).
9. Shokrizadeh, R., Saghaei, A., and Yaquninejad, Y. "An evaluation of an adaptive generalized likelihood ratio charts for monitoring the process mean", International Journal of Applied Operational Research, 6(3), pp. 59-68 (2016).
10. Yang, S.F. and Arnold, B.C. "A simple approach for monitoring process mean and variance simultaneously", Frontiers in Statistical Quality Control, 11, Springer International Publishing, pp. 135-149 (2015).
11. Chen, G., Cheng, S.W., and Xie, H. "Monitoring process mean and variability with one EWMA chart", Journal of Quality Technology, 33(2), pp. 223-233 (2001).
12. Apley, D.W. and Shi, J. "The GLRT for statistical process control of autocorrelated processes", IIE Transactions, 31, pp. 1123-1134 (1999).
13. Lu, C.W. and Reynolds, M.R. "EWMA control charts for monitoring the mean of autocorrelated processes", Journal of Quality Technology, 31(2), pp. 166-188 (1999).
14. Zhang, W., Jiao, J., Yang, M., et al. "An enhanced adoptive CUSUM control chart", IIE Transactions, 41(7), pp. 642-653 (2009).
15. Oppenheim, A.V., Wilsky, A.S., and Hamid, S., Signal and Systems, Pearson New International Edition (2014).
16. Wang, K., Chen, J., and Song, Z. "Data-driven sensor fault diagnosis systems for linear feedback control loops", Journal of Process Control, 54, pp. 152- 171(2017).
17. Chen, M., Xu, G., Yan, R., et al. "Detecting scalar intermittent faults in linear stochastic dynamic systems", International Journal of System Science, 46(8), pp. 1337-1348 (2015).
18. Zuo, C., Song, X., and Park, J.H. "Linear estimation for system with unknown measurement input and missing measurement", Chinese Automation Congress (CAC), Jinan, China (2017).
19. Liu, W. and Shi, P. "Optimal linear filtering for networked control systems with time-correlated fading channels", Automatica, 101, pp. 345-353 (2018).
20. Liu, W., Zhang, H., Yu, K., et al. "Optimal linear filtering for networked systems with communication constraints, fading measurements, and multiplicative noises", International Journal of Adaptive Control and Signal Processing, 31(7), pp. 1019-1039 (2016).
21. Eijnden, V.D., Knops, Y., and Heertjes, M.F. "A hybrid integrator-gain based low-pass filter for nonlinear motion control", Conference on Control Technology and Applications (CCTA), Copenhagen, Denmark (2018).
22. Box, G.E.P., Jenkins, G.M., and Reinsel, G.C., Time Series Analysis, Forecasting and Control, Prentice-Hall International, New Jersey (1994).
23. English, J.R. and Case, K.E. "Control charts applied as filtering devices within feedback control loop", IIE Transactions, 22(3), pp. 255-269 (1990).
24. Smith, C.A. and Corripio, A.B., Principals and Practice of Automatic Process Control, John Wiley and Sons, New York (1997).
25. Chang, Y.M. and Wu., T.L. "On the average run length of control charts for autocorrelated processes", Methodology and Computing in Applied Probability, 13(2), pp. 419-431 (2011).
26. Fu, J.C. and Spring, F. "On the average run length of quality control schemes using a Markov chain approach", Statistics & Probability Letters, 56, pp. 369- 380 (2002).
27. Bohm, W. and Hackl, P. "The effect of serial correlation on the in-control average run length of cumulative score charts", Journal of Statistical Planning and Inferences, 54, pp. 15-30 (1996).
28. Jiang, W., Tsui, K.L., and Woodall, W.H. "A new SPC monitoring method: The ARMA chart", Technometrics, 42(4), pp. 399-410 (2000).