A new nonparametric composite exponentially weighted moving average sign control chart

Document Type : Article

Authors

1 Department of Statistics, Government College University Faisalabad, Faisalabad 38000, Pakistan

2 Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia

3 Department of Statistics, Government College University Lahore, Pakistan

4 College of Statistical and Actuarial Sciences, University of the Punjab Lahore, Pakistan

Abstract

In this paper, a new nonparametric control chart based on two EWMA statistics is proposed for monitoring process deviation from the target value. The performance comparison of the proposed chart with the existing nonparametric EWMA sign control chart and a nonparametric CUSUM mean control chart are made by using out-of-control average run length. The simulation study showed the superiority of the suggested chart over the four other parametric and nonparametric charts. An empirical illustration is also provided for performance evaluation of the proposed chart. By comparing the proposed chart with the existing charts, it is concluded that the proposed chart is more sensitive in detecting a small shift in the process.

Keywords


References:
1. Qiu, P., Introduction to Statistical Process Control, Boca Raton, FL: CRC Press (2013).
2. Shewhart, W. "Economic quality control of manufactured product", Bell System Technical Journal, 9(2), pp. 364-389 (1930).
3. Page, E.S. "Continuous inspection schemes", Biometrika, 41(1/2), pp. 100-115 (1954).
4. Roberts, S. "Control chart tests based on geometric moving averages", Technometrics, 1(3), pp. 239-250 (1959).
5. Lucas, J.M. "Combined Shewhart-CUSUM quality control schemes", Journal of Quality Technology, 14(2), pp. 51-59 (1982).
6. Lucas, J.M. and Saccucci, M.S. "Exponentially weighted moving average control schemes: properties and enhancements", Technometrics, 32(1), pp. 1-12 (1990).
7. Abbas, N., Riaz, M., and Does, R.J. "Mixed exponentially weighted moving average-cumulative sum charts for process monitoring", Quality and Reliability Engineering International, 29(3), pp. 345-356 (2013).
8. Haq, A. "A new hybrid exponentially weighted moving average control chart for monitoring process mean", Quality and Reliability Engineering International, 29(7), pp. 1015-1025 (2013).
9. Haq, A. "A new hybrid exponentially weighted moving average control chart for monitoring process mean: discussion", Quality and Reliability Engineering International, 33(7), pp. 1629-1631 (2017).
10. Human, S.W., Kritzinger, P., and Chakraborti, S."Robustness of the EWMA control chart for individual observations", Journal of Applied Statistics, 38(10), pp. 2071-2087 (2011).
11. Chakraborti, S. and Graham, M.A., Nonparametric Statistical Process Control, John Wiley & Sons (2019).
12. Yang, S.-F. and Cheng, S.W. "A new non-parametric CUSUM mean chart", Quality and Reliability Engineering International, 27(7), pp. 867-875 (2011).
13. Yang, S.-F., Lin, J.-S., and Cheng, S.W. "A new nonparametric EWMA sign control chart", Expert Systems with Applications, 38(5), pp. 6239-6243 (2011).
14. Liu, L., Chen, B., Zhang, J., et al. "Adaptive phase II nonparametric EWMA control chart with variable sampling interval", Quality and Reliability Engineering International, 31(1), pp. 15-26 (2015).
15. Lu, S.L. "An extended nonparametric exponentially weighted moving average sign control chart", Quality and Reliability Engineering International, 31(1), pp. 3-13 (2015).
16. Abbasi, S.A., Ahmad, S., and Riaz, M. "On enhanced sensitivity of nonparametric EWMA control charts for process monitoring", Scientia Iranica, 24(1), pp. 424- 438 (2017).
17. Abbasi, A., Aslam, M., and Saghir, A. "A mixed nonparametric control chart for efficient process monitoring", The International Journal of Advanced Manufacturing Technology, 99, pp. 2549-2561 (2018).
18. Haq, A. "A new nonparametric synthetic EWMA control chart for monitoring process mean", Communications in Statistics-Simulation and Computation, 48(6), pp. 1665-1676 (2019).
19. Raza, M.A., Nawaz, T., and Han, D. "On designing distribution-free homogeneously weighted moving average control charts", Journal of Testing and Evaluation, 48(4), pp. 3154-3171 (2020).
20. Altukife, F.S. "A new nonparametric control chart based on the observations exceeding the grand median", Pakistan Journal of Statistics, 19(3), pp. 343- 352 (2003).
21. Altukife, F.S. "Nonparametric control chart based on sum of ranks", Pakistan Journal of Statistics, 19(3), pp. 291-300 (2003).
22. Amin, R.W., Reynolds Jr, M.R., and Saad, B. "Nonparametric quality control charts based on the sign statistic", Communications in Statistics-Theory and Methods, 24(6), pp. 1597-1623 (1995).
23. Aslam, M., Raza, M.A., Azam, M., et al. "Design of a sign chart using a new EWMA statistic", Communications in Statistics-Theory and Methods, 49(6), pp. 1299-1310 (2020).
24. Bakir, S.T. "A distribution-free Shewhart quality control chart based on signed-ranks", Quality Engineering, 16(4), pp. 613-623 (2004).
25. Bakir, S.T. "Distribution-free quality control charts based on signed-rank-like statistics", Communications in Statistics-Theory and Methods, 35(4), pp. 743-757 (2006).
26. Bakir, S.T. "A nonparametric shewhart-type quality control chart for monitoring broad changes in a process distribution", International Journal of Quality, Statistics, and Reliability, 2012 (2012).DOI: https://doi.org/10.1155/2012/147520.
27. Chowdhury, S., Mukherjee, A., and Chakraborti, S. "Distribution-free phase II CUSUM control chart for M.A. Raza et al./Scientia Iranica, Transactions E: Industrial Engineering 29 (2022) 290-302 301. joint monitoring of location and scale", Quality and Reliability Engineering International, 31(1), pp. 135- 151 (2015).
28. Graham, M.A., Chakraborti, S., and Human, S.W. "A nonparametric EWMA sign chart for location based on individual measurements", Quality Engineering, 23(3), pp. 227-241 (2011).
29. Graham, M.A., Chakraborti, S., and Human, S.W. "A nonparametric exponentially weighted moving average signed-rank chart for monitoring location", Computational Statistics & Data Analysis, 55(8), pp. 2490-2503 (2011).
30. Graham, M.A., Chakraborti, S., and Mukherjee, A. "Design and implementation of CUSUM exceedance control charts for unknown location", International Journal of Production Research, 52(18), pp. 5546-5564 (2014).
31. Graham, M.A., Mukherjee, A., and Chakraborti, S. "Distribution-free exponentially weighted moving average control charts for monitoring unknown location", Computational Statistics & Data Analysis, 56(8), pp. 2539-2561 (2012).
32. Koutras, M.V. and Triantafyllou, I.S. "A general class of nonparametric control charts", Quality and Reliability Engineering International, 34(3), pp. 427- 435 (2018).
33. Mahmood, T., Nazir, H.Z., Abbas, N., et al. "Performance evaluation of joint monitoring control charts", Scientia Iranica, 24(4), pp. 2152-2163 (2017).
34. Raza, M.A., Nawaz, T., Aslam, M., et al. "A new nonparametric double exponentially weighted moving average control chart", Quality and Reliability Engineering International, 36(1), pp. 68-87 (2020).
35. Riaz, M. and Abbasi, S.A. "Nonparametric double EWMA control chart for process monitoring", Revista Colombiana de Estadstica, 39(2), pp. 167-184 (2016).
36. Montgomery, D.C., Introduction to Statistical Quality Control, 7th Edn., Hoboken, NJ: John Wiley & Sons (2013).
Volume 29, Issue 1
Transactions on Industrial Engineering (E)
January and February 2022
Pages 290-302
  • Receive Date: 03 March 2019
  • Revise Date: 06 April 2020
  • Accept Date: 06 June 2020