An efficient mixed-memory-type control chart for normal and non-normal processes

Document Type : Article

Authors

1 Department of Statistics, University of Sargodha, Sargodha, 40100, Pakistan

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

3 Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

Abstract

Statistical process control techniques are commonly used to monitor process performance. Control charting technique is the most sophisticated tool of SPC and is categorized as memory-less and memory-type control charts. Shewhart-type control charts have low efficiency in detecting the small changes in the process parameters and named as memory-less control charts, and memory-type control charts (for example cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts) are very sensitive to small persistent shifts. In connection with enhancing the performance of CUSUM and EWMA charts, an efficient variant of memory-type charts for the location parameter is developed based on mixing the double exponentially weighted moving average (DEWMA) chart and CUSUM chart by performing exponential smoothing twice. Performance of the proposed efficient variant is compared with existing counterparts under normal and non-normal (heavy tails and skewed) environments. The study also provides an industrial application related to the monitoring of weights of quarters made by mint machine placed into service at U.S. Mint. From theoretical and numerical studies, it is revealed that proposed variant of memory-type charts outperforms the counterparts in detecting shifts of small and moderate magnitude.

Keywords

Main Subjects

References

  1. References:

    1. Page ES. “Continuous inspection schemes”, Biometrika, 41(1), pp.100–115 (1954).
    2. Roberts SW. “Control chart tests based on geometric moving averages”, Technometrics, 3(1), pp. 239-250 (1959).
    3. Abbas, N. “Homogeneously weighted moving average control chart with an application in substrate manufacturing process”, Computers and Industrial Engineering, 120(6), pp.460-470 (2018).
    4. Zaman, B., Riaz, M., Lee, M. H. “On the performance of control charts for simultaneous monitoring of location and dispersion parameters”, Quality and Reliability Engineering International, 33(1), pp. 37-56 (2016).
    5. Abid M, Nazir ZA, Riaz M, et al. “Use of ranked set sampling in nonparametric control charts”, Journal of the Chinese Institute of Engineers, 39(5), pp. 1-19 (2016).
    6. Abid M, Nazir ZA, Riaz M, et al. “Investigating the impact of ranked set sampling in nonparametric CUSUM control charts”, Quality and Reliability Engineering International, 33(1), pp. 203-214 (2017).
    7. Abid M, Nazir ZA, Riaz M, et al. “An efficient nonparametric EWMA Wilcoxon signed-rank chart for monitoring location”, Quality and Reliability Engineering International, 33(3), pp. 665-679 (2017).
    8. Lucas JM. “Combined Shewhart-CUSUM quality control schemes”, Journal of Quality Technology, 14(2), pp. 51-59 (1982).
    9. Lucas JM, Saccucci MS. “Exponentially weighted moving average control schemes: properties and enhancements”, Technometrics, 32(1), pp. 1–12 (1990).
    10. Abid M, Nazir ZA, Riaz M, et al. “In-control robustness comparison of different control charts”, Transaction of the Institute of Measurement and Control, 40(13), pp. 3860-3871 (2018).
    11. Raza, S. M. M., Riaz, M., Ali, S. “EWMA control chart for Poisson–exponential lifetime distribution under type I censoring”, Quality and Reliability Engineering International, 32(3), pp. 995-1005 (2016).
    12. Abujiya, M. R., Abbasi, S. A., Riaz, M. “A new EWMA control chart for monitoring Poisson observations. average control chart for monitoring the coefficient of variation”, Computers and Industrial Engineering, 78, pp. 205-212 (2016).
    13. Riaz, S., Riaz, M., Hussain, Z., et al. “Monitoring the performance of Bayesian EWMA control chart using loss functions”, Computers and Industrial Engineering, 112, pp. 426-436 (2018).
    14. Mehmood, R., Lee, M.H., Hussain, S., et al. “On efficient construction and evaluation of runs rules based control chart for known and unknown parameters
      under different distributions”, Quality and Reliability Engineering International, 35(2), pp.582-599 (2019).
    15. Shamma SE, Shamma AK. “Development and evaluation of control charts using double exponentially weighted moving averages”, International Journal of Quality and Reliability Management, 9(6), pp. 18-25 (1992).
    16. Riaz M, Abbas N, Does RJMM. “Improving the performance of CUSUM charts”, Quality and Reliability Engineering International, 27(4), pp. 415 – 424 (2011).
    17. Abbas N, Riaz M, Does RJMM. “Enhancing the performance of EWMA charts”, Quality and Reliability Engineering International, 27(6), pp. 821 – 833 (2011).
    18. Abbas N, Riaz M, Does RJMM. “Mixed exponentially weighted moving average- cumulative sum charts for process monitoring”, Quality and Reliability Engineering International, 29(3), pp. 355 – 365 (2013).
    19. Zaman B, Riaz M, Does RJMM. “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 (2014).
    20. Nazir HZ, Riaz M, Does RJMM, et al. “Robust CUSUM control charting”, Quality Engineering, 25(3), pp. 211-224 (2013).
    21. Ahmad L, Aslam M, Jun CH. “Designing of X-bar control charts based on  process capability index using repetitive sampling”, Transactions of the Institute of Measurement and Control, 36(3), pp. 367-374 (2014).
    22. Riaz M, Ali S. “On process monitoring using location control charts under different loss functions”, Transactions of the Institute of Measurement and Control, 38(9), pp. 1107-1119 (2015).
    23. Abujiya MR, Lee MH, Riaz M. “New EWMA S2 control charts for monitoring process dispersion”, Scientia Iranica, 24(1), pp. 378-389 (2017).
    24. Abbasi SA, Ahmad S, Riaz M. “On enhanced sensitivity of nonparametric EWMA control charts for process monitoring”, Scientia Iranica, 24(3), pp. 1603-1614 (2017).
    25. Ajadi JO, Riaz M. “New memory-type control charts for monitoring process mean and dispersion”, Scientia Iranica, 24(6), pp. 3423-3438 (2017).
    26. Hussain S, Song L, Ahmad S, et al. “On auxiliary information based improved EWMA median control charts”, Scientia Iranica, 25(2), pp. 954-982 (2018).
    27. Zhang L, Chen G. “An extended EWMA mean chart”, Quality Technology and Quality Management, 2(1), pp. 39-52 (2005).
    28. Triola MF. “Elementary Statistics U sing Excel”, Pearson and Addison Wesley, Boston (2004).
Scientia Iranica
Volume 28, Issue 3 - Serial Number 3
Transactions on Industrial Engineering (E)
May and June 2021
Pages 1736-1749

Files

History

  • Receive Date: 01 August 2018
  • Revise Date: 21 April 2019
  • Accept Date: 14 September 2019

Share

How to cite

Statistics