On the Performance of the Extended EWMA Control Chart for Monitoring Process Mean Based on Autocorrelated Data

Main Article Content

Kotchaporn Karoon
Yupaporn Areepong
Saowanit Sukparungsee

Abstract

The extended exponentially weighted moving average (EEWMA) control chart is an instrument for detection. It can quickly identify small shifts in the process. The benchmark for the control chart's performance is the average run length (ARL). In this paper, we present the efficiency of the EEWMA control chart to detect tiny shifts when the observations are autocorrelated with exponential residuals through the explicit formulas of the ARL. The accuracy of the solution was verified with the numerical integral equation (NIE) method. After that, the ARL effectiveness of the ARL on the EEWMA control chart was expanded to compare with the traditional EWMA control chart. Finally, using two real datasets that indicate the percentages of internet users using Windows 7 and iOS, the applicability of the offered method is shown. Our findings support the notion that the EEWMA control chart performs better when using autocorrelated data to track tiny changes.

Article Details

How to Cite
Karoon, K., Areepong, Y., & Sukparungsee, S. (2024). On the Performance of the Extended EWMA Control Chart for Monitoring Process Mean Based on Autocorrelated Data. Applied Science and Engineering Progress, 17(2), 6599. https://doi.org/10.14416/j.asep.2023.01.004
Section
Research Articles

References

S. Ozilgen, “Statistical quality control charts: New tools for studying the body mass index of populations form the young to the elderly,” Nutrition, Health & Aging, vol. 15, no. 5, pp. 333–339, 2011.

M. Kovarik, L. Sarga, and P. Klimek, “Usage of control charts for time series analysis in financial management,” Business Economics and Management, vol. 16, no. 1, pp. 138–158, 2015.

W. A. Shewhart, Economic Control of Quality of Manufactured Product. New York: Van Nostrand, 1931.

W. S. Roberts, “Control chart tests based on geometric moving average,” Technometrics, vol. 1, no. 3, pp. 239–250, 1959.

E. S. Page, “Continuous inspection schemes,” Biometrika, vol. 41, no. 1–2, pp. 100–115, 1954.

A. K. Patel and J. Divecha, “Modified exponentially weighted moving average (EWMA) control chart for an analytical process data,” Chemical Engineering and Materials Science, vol. 2, pp. 12–20, 2011.

N. Khan, M. Alsam, and C.H. Jun, “Design of a control chart using a modified EWMA statistics,” Quality and Reliability Engineering International, vol. 33, no. 5, pp. 1095–1104, 2017.

M. Neveed, M. Azam, N. Khan, and M. Aslam, “Design a control chart using extended EWMA statistic,” Technologies, vol. 6, no. 4, pp. 108– 122, 2018.

C. M. Mastrangelo and D. C. Montgomery, “SPC with correlated observations for the chemical and process industries,” Quality Reliability Engineering International, vol. 11, no. 2, pp. 79–89, 1995.

C. Chananet, Y. Areepong, and S. Sukparungsee, “A Markov chain approach for average run length of EWMA and CUSUM control chart based on ZINB model,” International Journal of Applied Mathematics and Statistics, vol. 53, no. 1, pp. 126–137, 2015.

S. Sukparungsee, “Combining martingale and integral equation approaches for finding optimal parameters of EWMA,” Applied Mathematical Sciences, vol. 6, pp. 4471–4482, 2012.

K. Karoon, Y. Areepong, and S. Sukparungsee, “Numerical integral equation methods of average run length on extended EWMA control chart for autoregressive process,” in International Conference on Applied and Engineering Mathematics, 2021, pp. 51–56.

W. Suriyakat, Y. Areepong, S. Sukparungsee, and G. Mititelu, “Analytical method of average run length for trend exponential AR(1) processes in EWMA procedure,” IAENG International Journal of Applied Mathematics, vol. 42, no. 4, pp. 250–253, 2012.

K. Petcharat, Y. Areeporng, and S. Sukparungsee, “Exact solution of average run length of EWMA chart for MA(q) processes,” Far East Journal of Mathematical Sciences, vol. 2, no. 2, pp. 291–300, 2013.

P. Busababodin, “An analytical expression to CUSUM chart for seasonal AR(p) model,” Far Fast Journal of Mathematical Sciences, vol. 88, no. 1, pp. 89–105, 2014.

P. Paichit, “Exact expression for average run length of control chart of ARX(p) procedure,” KKU Science Journal, vol. 45, no. 4, pp. 948– 958, 2017.

S. Phanyaem, “Average run length of cumulative sum control charts for SARMA(1,1)L models,” Thailand Statistician, vol. 15, pp. 184–195, 2017.

S. Sukparungsee and Y. Areepong, “An explicit analytical solution of the average run length of an exponentially weighted moving average control chart using an autoregressive model,” Chiang Mai Journal of Science, vol. 44, no. 3, pp. 1172–1179, 2017.

Y. Areepong, “Explicit formulas of average run length for a moving average control chart monitoring the number of defective products,” IJAM, vol.80, pp. 331–343, 2019.

S. M. Anwar, M. Aslam, S. Ahmad, and M. Riaz, “A modified-mxEWMA location chart for the improved process monitoring using auxiliary information and its application in wood industry,” Quality Technology and Quantitative Management, vol. 17, no. 5, pp. 561–579, 2020.

R. Sunthornwat and Y. Areepong, “Average run length on CUSUM control chart for seasonal and non-seasonal moving average processes with exogenous variable,” Symmetry, vol. 12, no. 1, pp. 173–187, 2020.

A. Saghir, M. Aslam, A. Faraz, and L. Ahmad, “Monitoring process variation using modified EWMA,” Quality and Reliability Engineering International, vol. 36, no. 1, pp. 328–339, 2020.

P. Phanthuna, Y. Areepong, and S. Sukparungsee, “Exact run length evaluation on a two-sided modified exponentially weighted moving average chart for monitoring process mean,” Computer Modeling in Engineering and Sciences, vol. 127, no. 1, pp. 23–41, 2021.

P. Phanthuna, Y. Areepong, and S. Sukparungsee, “Detection capability of the modified EWMA chart for the trend stationary AR(1) model,” Thailand Statistician, vol. 19, no. 1, pp. 70–81, 2021.

K. Karoon, Y. Areepong, and S. Sukparungsee, “Exact run length evaluation on extended EWMA control chart for autoregressive process,” Intelligent Automation and Soft Computing, vol. 33, no. 2, pp. 743–758, 2022.

C. W. Champ and S. E. Rigdon, “A comparison of the Markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts,” Communications in Statistics-Simulation and Computation, vol. 20, no. 1, pp. 191–203, 1991.

Q. T. Nguyen, K. P. Tran, P. Castagliola, G. Celano, and S. Lardiane, “One-sided synthetic control charts for monitoring the multivariate coefficient of variation,” Journal of Statistical Computation and Simulation, vol. 89, no. 1, pp. 1841–1862, 2019.

A. Tang, P. Castagliola, J. Sun, and X. Hu, “Optimal design of the adaptive EWMA chart for the mean based on median run length and expected median run length,” Quality Technology and Quantitative Management, vol. 16, no. 4, pp. 439–458, 2018.