Developing mixed EWMA-CUSUM and CUSUM-EWMA control charts based on MRSS and DRSS procedures

Document Type : Article

Authors

Department of Industrial Engineering, Shahed University, Tehran, Iran

Abstract

The mixed EWMA-CUSUM and CUSUM-EWMA control charts are among the control charts provided in recent years by combining two exponentially weighted moving average and cumulative sum charts for efficient monitoring of the process mean. In this paper, we extended these mixed control charts by using new median ranked set sampling and double ranked set sampling procedures. The performance of the proposed mixed control charts is evaluated through extensive Monte Carlo simulations in terms of average run length criterion and the results show the proposed charts outperform the similar charts for detecting different shifts in process mean. Furthermore, a real data-set is also presented for explaining the implementation of the proposed control charts.

Keywords


References:
1. Shewhart, W.A. "Some applications of statistical methods to the analysis of physical and engineering data", Bell System Technical Journal, 3(1), pp. 43-87 (1924).
2. Roberts, S.W. "Control chart tests based on geometric moving averages", Technometrics, 1(3), pp. 239-250 (1959).
3. Page, E.S. "Cumulative sum charts", Technometrics, 3(1), pp. 1-9 (1951).
4. Lucas, J.M. "Combined shewhart-cusum quality control schemes", Journal of Quality Technology, 14(2), pp. 51-59 (1982).
5. Lucas, J.M. and Saccucci, M.S. "Exponentially weighted moving average control schemes properties and enhancements", Technometrics, 32(1), pp. 1-12 (1990).
6. Jiang, W., Shu, L., and Apley, D.W. "Adaptive CUSUM procedures with EWMA-based shift estimators", IIE Transactions, 40(10), pp. 992-1003 (2008).
7. Abbas, N., Riaz, M., and J.M.M, R. "Mixed exponentially weighted moving average-cumulative sum charts for process monitoring", Quality and Reliability Engineering International, 29(3), pp. 345-356 (2013).
8. Riaz, M., Zaman, B., Abbas, N., et al. "Mixed cumulative sum-exponentially weighted moving average control charts: an efficient way of monitoring process location", Quality and Reliability Engineering International, 31(8), pp. 1407-1421 (2015).
9. Aslam, M.A. "Mixed EWMA-CUSUM control chart for weibull-distributed quality characteristics", Quality and Reliability Engineering International, 32(8), pp. 2987-2994 (2016).
10. Osei-Aning, R., Abbasi, S.A., and Riaz, M. "Mixed EWMA-CUSUM and mixed CUSUM-EWMA modified control charts for monitoring first order autoregressive processes", Quality Technology & Quantitative Management, 14(4), pp. 429-453 (2017).
11. Riaz, M., Khaliq, Q.U.A., and Gul, S. "Mixed Tukey EWMA-CUSUM control chart and its applications", Quality Technology & Quantitative Management, 14(4), pp. 429-453 (2017).
12. Ajadi, J.O. and Riaz, M. "Mixed multivariate EWMACUSUM control charts for an improved process monitoring", Communications in Statistics - Theory and Method, 46(14), pp. 6980-6993 (2017).
13. Aslam, M., Azam, M., and Jun, C.H. "A HEWMACUSUM control chart for the Weibull distribution", Communications in Statistics - Theory and Methods, 47(24), pp. 5973-5985 (2018).
14. Abbas, N., Raji, I.A., Riaz, M., et al. "Designing mixed EWMA Dual-CUSUM chart with applications in petro-chemical industry", IEEE Access, 6, pp. 78931-78946 (2018).
15. Riaz, M., Ajadi, J.O., Mahmood, T., et al. "Multivariate mixed EWMA-CUSUM control chart for monitoring the process variance-covariance matrix", IEEE Access, 7, pp. 100174-100186 (2019).
16. Rao, G.S., Aslam, M., and Rasheed, U. "Mixed EWMA-CUSUM chart for COM-Poisson distribution", Journal of Statistics and Management Systems, 23(3), pp. 511-527 (2020).
17. McIntyre, G.A. "A method for unbiased selective F, using ranked sets", Australian Journal of Agriculture Research, 3(4), pp. 385-390 (1952).
18. Salazar, R.D. and Sinha, A.K. "Control chart x-bar based on ranked set sampling", Comunicacion Tecica,, No. 1-97-09 (PE/CIMAT) (1977).
19. Muttlak, H.A. and Al-Sabah, W.S. "Statistical quality control based on ranked set sampling", Journal of Applied Statistics, 30(9), pp. 1055-1078 (2003).
20. Abujiya, M.R. and Muttlak, H.A. "Monitoring the process mean and variance using ranked set sampling and its modifications", Journal of Statistical Theory and Applications, 6(4), pp. 408-422 (2007).
21. Mehmood, R., Riaz, M., and Does, R.J.M.M. "Control charts for location based on different sampling schemes", Journal of Applied Statistics, 40(3), pp. 483-494 (2013).
22. Al-Sabah, W.S. "Cumulative sum statistical control charts using ranked set sampling data", Pakistan Journal of Statistics,  26(2), pp. 365-378 (2010).
23. Abujiya, M.R. and Lee, M.H. "The three statistical control charts using ranked set sampling", 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO) (2013). DOI:10.1109/ICMSAO.2013.6552684.
24. Haq, A., Brown, J., and Moltchanova, E. "Improved exponentially weighted moving average control charts for monitoring process mean and dispersion", Quality and Reliability Engineering International, 31(2), pp. 217-237 (2015).
25. Awais, M. and Haq, A. "An EWMA chart for monitoring process mean", Journal of Statistical Computation and Simulation, 88(5), pp. 1003-1025 (2018).
26. Haq, A. and Munir, W. "Improved CUSUM charts for monitoring process mean", Journal of Statistical Computation and Simulation, 88(9), pp. 1684-1701 (2018).
27. Abbasi, S.A. "Location charts based on ranked set sampling for normal and non-normal processes", Published online in Quality and Reliability Engineering International (2019). DOI: 10.1002/qre.2463.
28. Cochran, W.G., Sampling Techniques, 3rd Edition, John Wiley & Sons (1997).
29. Wolfe, D.A. "Ranked set sampling: An approach to more efficient data collection", Statistical Science, 19(4), pp. 636-643 (2004).
30. Al-Saleh, M.F. and Al-Kadiri, M.A. "Double-ranked set sampling", Statistics & Probability Letters, 48(2), pp. 205-212 (2000).
31. Muttlak, H.A. "Median ranked set sampling", Journal of Applied Statistical Sciences, 66, pp. 245-255 (1997).
32. Montgomery, D.C., Introduction to Statistical Quality Control, 6th Edition, John Wiley & Sons, New York (2009).
Volume 29, Issue 5
Transactions on Industrial Engineering (E)
September and October 2022
Pages 2756-2771
  • Receive Date: 14 March 2020
  • Revise Date: 09 August 2020
  • Accept Date: 03 October 2020