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Development of a New MEWMA – Wilcoxon Sign Rank Chart for Detection of Change in Mean Parameter

Kanita Petcharat, Saowanit Sukparungsee


A nonparametric chart has been accepted and implemented for real world problems, especially, when the distribution of the population is unknown and the parameter could not be estimated. The nonparametric chart can overcome those limitations and it is user-friendly. Consequently, the objective of this research is to develop a new modified exponentially weighted moving average (MEWMA) chart based on Sign Rank statistics, namely MEWMA-SR, and to compare the performance of change detection with the EWMA and MEWMA charts and nonparametric EWMA based on the Sign (EWMA-Sign) and the Sign Rank (EWMA-SR), and MEWMA-Sign charts. The efficiency measurement of charts is commonly performed by average run length (ARL) divided into two states; in control ARL (ARL0) and out of control ARL (ARL1). The numerical results were carried out by Monte Carlo simulation with 105 replication and the best performance of the chart is considered by the minimum value of ARL1. The proposed chart outperforms when a subgroup is small and a magnitude of changes is moderate for Laplace, otherwise the EWMA-SR is superior to small changes. When the observations are from lognormal the MEWMA-SR performs better than EMWA-SR and other charts for moderate to large changes for all sizes of subgroups. Furthermore, the proposed chart is applied to real data set as the S&P 500 index and shows the best performance in detecting a change.


[1] S.-H. Kim and J. R. Wilsonin, “A discussion on ‘Detection of intrusions in information systems by sequential change-point methods’ by Tartakovsky, Rozovskii, Blažek, and Kim,” Statistical Methodology, vol. 3, pp. 315–319, 2006.

[2] B. Mason and J. Antony, “Statistical process control: An essential ingredient for improving service and manufacturing quality,” Managing Service Quality: An International Journal, vol. 10, pp. 233–238, 2000.

[3] R. R. Sitter, L. P. Hanrahan, D. De Mets, and H. A. Anderson, “A monitoring system to detect increased rates of cancer incidence,” American Journal of Epidemiology, vol. 132, pp. 123–130. 1990.

[4] M. Frisén, “Evaluations of methods for statistical surveillance,” Statistics in Medicine, vol. 11, pp. 1489–1502, 1992.

[5] M. Kovářík, L. Sarga, and P. Klímek, “Usage of control charts for time series analysis in financial management,” Journal of Business Economics and Management, vol. 16, no. 1, pp. 138–158, 2015, doi: 10.3846/16111699.2012.732106.

[6] M. Aslam, A. Shareef, and K. Khan, “Monitoring the temperature through moving average control under uncertainty environment,” Scientific Report, vol. 10, no. 1, 2020, Art. no. 12182, doi: 10.1038/ s41598-020-69192-8.

[7] M. Aslam, A. Shafqat, M. Albassam, J. C. Malela- Majika, and S. C. Shongwe, “A new CUSUM control chart under uncertainty with applications in petroleum and meteorology,” PLoS One, vol. 16, no. 2, 2021, Art. no. e0246185, doi: 10.1371/journal.pone.0246185.

[8] W. A. Shewhart, Economic Control of Quality of Manufactured Product. New York: D. Van Nostrand Company, 1931.

[9] D. C. Montgomery, Introduction to Statistical Quality Control Case Study. New York: John Wiley and Sons, 2008.

[10] E. S. Page, “Continuous inspection schemes,” Biometrika, vol. 41, pp. 100–144, 1954.

[11] S. W. Roberts, “Control chart tests based on geometric moving average,” Technometrics, vol. 1, pp. 239–250, 1959.

[12] M. B. C. Khoo, “A moving average control chart for monitoring the fraction nonconforming,” Quality and Reliability Engineering International, vol. 20, pp. 617–635, 2004.

[13] M. B. C. Khoo and V. H. Wong, “A double moving average control chart,” Communication in Statistics – Simulation and Computation, vol. 37, pp. 1696–1708, 2008.

[14] A. K. Patel and J. Divecha, “Modified exponentially weighted moving average (EWMA) control chart for an analytical process data,” Journal of Chemical Engineering and Materials Science, vol. 2, no. 1, pp. 12–20, 2011.

[15] S. Sukparungsee, Y. Areepong, and R. Taboran, “Exponentially weighted moving average – moving average charts for monitoring the process mean,” Plos One, vol. 15, no. 2, 2020, Art. no. e0228208, doi: 10.1371/journal.pone.0228208.

[16] N. Saengsura, S. Sukparungsee, and Y. Areepong, “Mixed moving average-cumulative sum control chart for monitoring parameter change,” Intelligent Automation and Soft Computing, vol. 31, no. 1, pp. 635–647, 2022, doi: 10.32604/ iasc.2022.019997.

[17] S. F. Yang, J. S. Lin, and S. W. Cheng, “A new non parametric EWMA sign control chart,” Expert Systems with Applications, vol. 38, no. 5, pp. 6239–6243, 2011, doi: 10.1016/ j.eswa.2010.11.044.

[18] R. Amin and A. J. Searcy, “A nonparametric exponentially weighted moving average control scheme,” Communication in Statistics-Simulation and Computation, vol. 20, no. 4, pp. 1049–1072, 1991.

[19] M. Aslam, M. A. Raza, M. Azam, L. Ahmad, and C.-H. Jun, “Design of a sign chart using a new EWMA statistic,” Communications in Statistics - Theory and Methods, vol. 49, no. 6, pp. 1299–1310, 2020, doi: 10.1080/03610926. 2018.1563163.

[20] R. Taboran and S. Sukparungsee, “An enhanced performance to monitor process mean with modified exponentially weighted moving average – signed control chart,” Applied Science and Engineering Progress, vol. 15, no. 4, 2022, Art. no. 5532, doi: 10.14416/j.asep.2021.10.013.

[21] M. A. Raza, T. Nawaz, and D. Han, “On designing distribution-free homogeneously weighted moving average control charts,” Journal of Testing and Evaluation, vol. 48, no. 4, pp. 3154– 3171, 2020, doi: 10.1177/ 0142331220973569.

[22] R Foundation for Statistical Computing, “R: A language and environment for statistical computing,” 2021. [Online]. Available: http://

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DOI: 10.14416/j.asep.2022.05.005


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