Document Type : Research Paper


1 School of Industrial Engineering, Purdue University, United States.

2 Department of Industrial and Entrepreneurial Engineering and Engineering Management, Western Michigan University, United States.


Exponential Weighted Moving Average (EWMA) control charts have been widely used in Statistical Process Control (SPC) to detect small and persistent process shifts. In theory, EWMA control limits monotonically increase over time to account for the continual growth of the EWMA statistic’s variance. However, these control limits are often assumed constant and are set to their respective asymptotic limits to simplify the process of applying and analyzing EWMA control charts. One-sided EWMA charts are often implemented when it is only desirable to detect shifts in a specific direction. When using one-sided EWMA charts, reflecting boundaries (resets) can be used to prevent the statistic from drifting too far from the chart’s control limit, which can delay shift detection. There have been several research efforts into designing and studying the performance of one-sided EWMA charts with reflecting boundaries. However, these efforts have maintained the constant control limit assumption. When implementing a reflecting boundary, the EWMA statistic’s variance is constantly being reset to zero, which may significantly affect the constant control limit assumption’s validity. The focus of this paper is to understand behavior of the one-sided EWMA control charts with constant and time-varying limit assumption through simulation studies.


Main Subjects

  1. Roberts, S. W. (1958). Properties of control chart zone tests. Bell system technical journal37(1), 83-114.
  2. Roberts, S. W. (1966). A comparison of some control chart procedures. Technometrics8(3), 411-430.
  3. Lorden, G. (1971). Procedures for reacting to a change in distribution. The annals of mathematical statistics, 42(6), 1897-1908.
  4. Brook, D. A. E. D., & Evans, D. (1972). An approach to the probability distribution of CUSUM run length. Biometrika59(3), 539-549.
  5. Robinson, P. B., & Ho, T. Y. (1978). Average run lengths of geometric moving average charts by numerical methods. Technometrics20(1), 85-93.
  6. Crowder, S. V. (1987). A simple method for studying run–length distributions of exponentially weighted moving average charts. Technometrics29(4), 401-407.
  7. Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: properties and enhancements. Technometrics32(1), 1-12.
  8. Gan, F. F. (1993). Exponentially weighted moving average control charts with reflecting boundaries. Journal of statistical computation and simulation46(1-2), 45-67.
  9. Shu, L., Jiang, W., & Wu, S. (2007). A one-sided EWMA control chart for monitoring process means. Communications in statistics—simulation and computation®36(4), 901-920.
  10. Joner Jr, M. D., Woodall, W. H., Reynolds Jr, M. R., & Fricker Jr, R. D. (2008). A one‐sided MEWMA chart for health surveillance. Quality and reliability engineering international24(5), 503-518.
  11. Gol-Ahmadi, N., & Raissi, S. (2018). Residual lifetime prediction for multi-state system using control charts to monitor affecting noise factor on deterioration process. Journal of applied research on industrial engineering5(1), 27-38.
  12. Saputra, T. M., Hernadewita, H., Prawira Saputra, A. Y., Kusumah, L. H., & ST, H. (2019). Quality improvement of molding machine through statistical process control in plastic industry. Journal of applied research on industrial engineering6(2), 87-96.
  13. Sunadi, S., Purba, H. H., & Saroso, D. S. (2020). Statistical Process Control (SPC) method to improve the capability process of drop impact resistance: a case study at aluminum cans manufacturing industry in Indonesia. Journal of applied research on industrial engineering7(1), 92-108.
  14. Calzada, M. E., & Scariano, S. M. (2003). Reconciling the integral equation and Markov chain approaches for computing EWMA average run lengths. Communications in statistics-simulation and computation32(2), 591-604.
  15. Petcharat, K., Areepong, Y., & Sukparungsee, S. (2013). Exact solution of average run length of EWMA chart for MA (q) processes. Far East journal of mathematical sciences78(2), 291.
  16. Woodall, W. H., & Mahmoud, M. A. (2005). The inertial properties of quality control charts. Technometrics47(4), 425-436.
  17. Capizzi, G., & Masarotto, G. (2010). Combined Shewhart–EWMA control charts with estimated parameters. Journal of statistical computation and simulation80(7), 793-807.