Impact of measurement error on mixed EWMA-CUSUM control chart

Document Type : Article


Department of Statistic, COMSATS University Islamabad, Lahore Campus


In statistical process control, measurement error plays an important role which is usually ignored. Measurement error can lead to incorrect conclusions about the performance of the process. In this paper, we examined the effect of measurement error on the shift detection ability of the mixed exponentially weighted moving average-cummulative sum (EWMA-CUSUM) control chart. We investigate the performance of mixed EWMA-CUSUM chart in case of mean shift by using (i) covariate method (ii) multiple measurement method (iii) linearly increasing variance method. The performance measuring tools such as average run length (ARL) and standard deviation of run length (SDRL) are estimated by using the Monte-Carlo simulation method. It is concluded that the performance of the mixed EWMA-CUSUM control chart is adversely effected by considering the measurement error. It is revealed from the comparative study that the mixed EWMA-CUSUM control chart is performing better than EWMA and CUSUM control charts in the presence of measurement error. An illustrative example is presented to demonstrate the performance of control charts in case of measurement error.


1. Roberts, S. "Control chart tests based on geometric moving averages", Technometrics, 1(3), pp. 239-250 (1959).
2. Page, E.S. "Continuous inspection schemes", Biometrika, 41(1/2), pp. 100-115 (1954).
3. 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).
4. Abujiya, M.A.R., Riaz, M., and Lee, M.H. "Enhancing the performance of combined Shewhart-EWMA charts", Quality and Reliability Engineering International, 29(8), pp. 1093-1106 (2013).
5. Zaman, B., Riaz, M., 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).
6. Ajadi, J.O., Riaz, M., and Al-Ghamdi, K. "On increasing the sensitivity of mixed EWMA-CUSUM control charts for location parameter", Journal of Applied Statistics, 43(7), pp. 1262-1278 (2016).
7. Riaz, A., Noor-ul-Amin, M., Shehzad, M.A., et al. "Auxiliary information based mixed EWMA-USUM mean control chart with measurement error", Iranian Journal of Science Technology, Transactions A: Science, 43(6), pp. 2937-2949 (2019).
8. Linna, K.W. and Woodall, W.H. "Effect of measurement error on Shewhart control charts", Journal of Quality Technology, 33(2), pp. 213-222 (2001).
9. Maravelakis, P., Panaretos, J., and Psarakis, S. "EWMA chart and measurement error", Journal of Applied Statistics, 31(4), pp. 445-455 (2004).
10. Mittag, H.-J. and Stemann, D. "Gauge imprecision effect on the performance of the XS control chart", Journal of Applied Statistics, 25(3), pp. 307-317 (1998).
11. Maravelakis, P.E. "Measurement error effect on the CUSUM control chart", Journal of Applied Statistics, 39(2), pp. 323-336 (2012).
12. Noor-ul-Amin, M., Riaz, A., and Safeer, A. "Exponentially weighted moving average control chart using auxiliary variable with measurement error", Communications in Statistics-Simulation and Computation (2019).
13. Ewan, W. and Kemp, K. "Sampling inspection of continuous processes with no autocorrelation between successive results", Biometrika, 47(3/4), pp. 363-380 (1960).
14. Montgomery, D.C., Introduction to Statistical Quality Control, John Wiley & Sons (New York) (2009).
15. Bennett, C.A. "Effect of measurement error on chemical process control", Industrial Quality Control, 10(4), pp. 17-20 (1954).
16. Hawkins, D.M. and Olwell, D.H., Cumulative Sum Charts and Charting for Quality Improvement, Springer Science & Business Media (2012).
17. Walden, C.T. "An analysis of variables control charts in the presence of measurement errors", Mississippi State University, Department of Industrial Engineering (1990).
18. Montgomery, D.C. and Runger, G.C. "Gauge capability and designed experiments. Part I: basic methods", Quality Engineering, 6(1), pp. 115-135 (1993).
19. Abbas, N. "Memory-type control charts in statistical process control", Universiteit van Amsterdam [Host] (2012).
20. Tran, K.P., Castagliola, P., and Balakrishnan, N. "On the performance of Shewhart median chart in the presence of measurement errors", Quality and Reliability Engineering International, 33(5), pp. 1019- 1029 (2017).