Monitoring coefficient of variation using variable sampling interval double exponentially weighted moving average charts

Document Type : Article

Authors

1 Institute of High-Quality Development Evaluation, Nanjing University of Posts and Telecommunications, Nanjing, China

2 School of Management, Nanjing University of Posts and Telecommunications, Nanjing, China

3 School of Management, Tianjin University of Commerce, Tianjin, China

4 Department of Mathematics, Liaoning University, Shenyang, China

5 School of Management Science and Engineering, Nanjing University of Finance and Economics, Nanjing, China

Abstract

As a measure of relative variability, the coefficient of variation (CV) is a valuable charting statistic in statistical process control. Great efforts have been devoted to monitoring CV efficiently. To further improve the performance of CV charts, this paper proposes three Double Exponentially Weighted Moving Average (DEWMA) charts by incorporating Variable Sampling Interval (VSI) strategies to monitor the CV squared. The run length properties of the proposed charts are evaluated via Monte Carlo simulations. Comparative studies show that the proposed VSI DEWMA CV charts detect the process shifts faster than the existing CV charts. A real data example is presented to illustrate the VSI DEWMA CV charts.

Keywords

References

References:
1. Yeong, W.C., Khoo, M.B.C., Tham, L.K., et al. "Monitoring the coefficient of variation using a variable sampling interval  EWMA chart", Journal of Quality Technology, 49(4), pp. 380-401 (2017). DOI: 10.1080/00224065.2017.11918004.
2. Kang, C.W., Lee, M.S., Seong, Y.J., et al. "A control chart for the coefficient of variation", Journal of Quality Technology, 39(2), pp. 151-158 (2007). DOI: 10.1080/00224065.2007.11917682.
3. Hong, E.-P., Kang ,C.-W., Baek, J.-W., et al. "Development of CV control chart using EWMA technique", Journal of the Society of Korea Industrial and Systems Engineering, 31(4), pp. 114-120 (2008).
4. Castagliola, P., Celano, G., and Psarakis, S. "Monitoring the coefficient of variation using EWMA charts", Journal of Quality Technology, 43(3), pp. 249-265 (2011). DOI: 10.1080/00224065.2011.11917861.
5. Calzada, M.E. and Scariano, S.M. "A synthetic control chart for the coefficient of variation", Journal of Statistical Computation and Simulation, 83(5), pp. 853-867 (2013). DOI: 10.1080/00949655.2011.639772.
6. Zhang, J., Li, Z., Chen, B., et al. "A new exponentially weighted moving average control chart for monitoring the coefficient of variation", Computers and Industrial Engineering, 78, pp. 205-212 (2014). https://doi.org/10.1016/j.cie.2014.09.027.
7. Zhang, J., Li, Z., and Wang, Z. "Control chart for monitoring the coefficient of variation with an exponentially weighted moving average procedure", Quality and Reliability Engineering International, 34(2), pp. 188-202 (2018). https://doi.org/10.1002/qre.2247.
8. Shu, L. and Jiang, W. "A new EWMA chart for monitoring process dispersion", Journal of Quality Technology, 40(3), pp. 319-331 (2008). DOI:10.1080/00224065.2008.11917737.
9. Haq, A. and Khoo, M.B.C. "New adaptive EWMA control charts for monitoring univariate and multivariate coefficient of variation", Computers and Industrial Engineering, 131, pp. 28-40 (2019). https://doi.org/10.1016/j.cie.2019.03.027.
10. Castagliola, P., Achouri, A., Taleb, H., et al. "Monitoring the coefficient of variation using control charts with run rules", Quality Technology and Quantitative Management, 10(1), pp. 75-94 (2013). DOI: 10.1080/16843703.2013.11673309.
11. Chen, R., Li, Z., and Zhang, J. "A generally weighted moving average control chart for monitoring the coefficient of variation", Applied Mathematical Modelling, 70, pp. 190-205 (2019). https://doi.org/10.1016/j.apm.2019.01.034.
12. Teoh, W.L., Khoo, M.B.C., Castagliola, P., et al. "Run-sum control charts for monitoring the coefficient of variation", European Journal of Operational Research, 257(1), pp. 144-158 (2017). https://doi.org/10.1016/j.ejor.2016.08.067.
13. Hu, X., Zhang, S., Zhou, X., et al. "The performance of double exponentially weighted moving average control charts for monitoring the coefficient of variation", Communications in Statistics-Simulation and Computation, 53(4), pp. 1-20 (2022). DOI: 10.1080/03610918.2022.2057539.
14. Jalilibal, Z., Amiri, A., Castagliola, P., et al. "Monitoring the coefficient of variation: A literature review", Computers and Industrial Engineering, p. 107600 (2021). https://doi.org/10.1016/j.cie.2021.107600.
15. Saccucci, M.S., Amin, R.W., and Lucas, J.M. "Exponentially weighted moving average control schemes with variable sampling intervals", Communications in Statistics - Simulation and Computation, 21(3), pp. 627-657 (1992). DOI: 10.1080/03610919208813040.
16. Shamma, S.E., Amin, R.W, Shamma AK. "A double exponentially weigiited moving average control procedure with variable sampling intervals", Communications in Statistics - Simulation and Computation, 20(2-3), pp. 511-528 (1991). DOI: 10.1080/03610919208813040.
17. Castagliola, P., Celano, G., Fichera, S., et al. "A variable sample size S2-EWMA control chart for monitoring the process variance", International Journal of Reliability, Quality and Safety Engineering, 15(03), pp. 181-201 (2008). DOI: 10.1142/s0218539308003039.
18. Haq, A. and Akhtar, S. "Auxiliary information based maximum EWMA and DEWMA charts with variable sampling intervals for process mean and variance", Communications in Statistics - Theory and Methods, 51(12), pp. 3985-4005 (2020). DOI: 10.1080/03610926.2020.1805766.
19. Reynolds, M.R., Amin, R.W., and Arnold, J.C. "CUSUM charts with variable sampling intervals", Technometrics, 32(4), pp. 371-384 (1990). DOI: 10.2307/1270114.
20. Reynolds, M.R. and Arnold, J.C. "EWMA control charts with variable sample sizes and variable sampling intervals", IIE Transactions, 33(6), pp. 511-530 (2001). DOI: 10.1080/00224065.2001.11980048.
21. Castagliola, P., Achouri, A., Taleb, H., et al. "Monitoring the coefficient of variation using a variable sampling interval control chart", Quality and Reliability Engineering International, 29(8), pp. 1135-1149 (2013). https://doi.org/10.1002/qre.1465.
22. Khaw, K.W., Khoo, M.B.C., Yeong, W.C., et al. "Monitoring the coefficient of variation using a variable sample size and sampling interval control chart", Communications in Statistics - Simulation and Computation, 46(7), pp. 5772-5794 (2017). DOI: 10.1080/03610918.2016.1177074.
23. Muhammad, A.N.B., Yeong, W.C., Chong, Z.L., et al. "Monitoring the coefficient of variation using a variable sample size EWMA chart", Computers and Industrial Engineering, 126, pp. 378-398 (2018). https://doi.org/10.1016/j.cie.2018.09.045.
24. Nguyen, H.D., Nguyen, Q.T., Tran, K.P., et al. "On the performance of VSI Shewhart control chart for monitoring the coefficient of variation in the presence of measurement errors", The International Journal of Advanced Manufacturing Technology, 104(1), pp. 211- 243 (2019). DOI: 10.1007/s00170-019-03352-7.
25. Tran, P.H. and Heuchenne, C. "Monitoring the coefficient of variation using variable sampling interval CUSUM control charts", Journal of Statistical Computation and Simulation, 91(3), pp. 501-521 (2021). DOI: 10.1080/00949655.2020.1819278.
26. Breunig, R. "An almost unbiased estimator of the coefficient of variation", Economics Letters, 70(1), pp. 15-19 (2001). https://doi.org/10.1016/S0165- 1765(00)00351-7.
27. Shamma, S.E. and Shamma, A.K. "Development and evaluation of control charts using double exponentially weighted moving averages", International Journal of Quality and Reliability Management, 9(6) (1992). DOI: 10.1108/02656719210018570.
28. Hamilton, M.D. and Crowder, S.V. "Average run lengths of EWMA control charts for monitoring a process standard deviation", Journal of Quality Technology, 24(1), pp. 44-50 (1992). DOI: 10.1080/00224065.1992.11979373.
29. Ryan, A.G. and Woodall, W.H. "Control charts for poisson count data with varying sample sizes", Journal of Quality Technology, 42(3), pp. 260-275 (2010). DOI: 10.1080/00224065.2010.11917823.
30. Xu, S. and Jeske, D.R. "Weighted EWMA charts for monitoring type I censored Weibull lifetimes", Journal of Quality Technology, 50(2), pp. 220-230 (2018). DOI: 10.1080/00224065.2018.1436830.
31. Dickinson, R.M., Roberts, D.A.O, Driscoll, A.R., et al. "CUSUM charts for monitoring the characteristic life of censored Weibull lifetimes", Journal of Quality Technology, 46(4), pp. 340-358 (2014). DOI:  10.1080/00224065.2014.11917976.
32. Qiu, P. and Li, Z. "Distribution-free monitoring of univariate processes", Statistics and Probability Letters, 81(12), pp. 1833-1840 (2011). 
Scientia Iranica
Volume 31, Issue 15
Transactions on Industrial Engineering (E)
July and August 2024
Pages 1293-1312

Files

Share

How to cite

Statistics