Performance Measurement of a DMEWMA Control Chart on an AR(p) Model with Exponential White Noise
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Abstract
The double-modified exponentially weighted moving average (DMEWMA) control chart running an autoregressive (AR) process is proposed to detect unusual events. The AR equation and the DMEWMA statistic are combined to evaluate the control limit of the exponential residual term to obtain the explicit formula for the average run length (ARL). The ARLs computed using the explicit formula approach and the well-established numerical integral equation method were compared to validate the former. The efficiencies of the original EWMA, MEWMA, and DMEWMA control charts running AR processes based on simulation and real data were compared by using the results of ARL and relative mean index calculations. The results indicate that the explicit formula for the ARL of an AR process running on a double-modified EWMA control chart detected changes more quickly than on either of the other two control charts for small and moderate changes. Finally, real data on COVID-19 is provided to demonstrate the application of this explicit formula.
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W. A. Shewhart, “Quality control charts,” The Bell System Technical Journal, vol. 5, no. 4, pp. 593–603, 1926, doi: 10.1002/j.1538-7305.1926.tb00125.x.
E. S. Page, “Continuous inspection schemes,” Biometrika, vol. 41, no. 1/2, pp. 100–115, 1954, doi: 10.2307/2333009.
S. W. Roberts, “Control chart tests based on geometric moving averages,” Technometrics, vol. 42, no. 1, pp. 97–101, 2000, doi: 10.1080/ 00401706.2000.10485986.
N. H. Irhaif, Z. I. Kareem, and S. M. Al-joboori, “Using the moving average and exponentially weighted moving average with COVID 19,” Periodicals of Engineering and Natural Sciences, vol. 9, no. 3, pp. 625–631, 2021, doi: 10.21533/pen.v9i3.2206.
A. Yupaporn and S. Rapin, “EWMA control chart based on its first hitting time and coronavirus alert levels for monitoring symmetric COVID-19 cases,” Asian Pacific Journal of Tropical Medicine, vol. 14, no. 8, pp. 364–374, 2021, doi: 10.4103/1995-7645.321613.
P. Kumari, A. Priyadarshi, A. K. Gupta, and S. K. Prasad, “Monitoring of the COVID-19 cases by EWMA control chart,” in International Conference on Innovative Computing and Communications, pp. 541–551, 2022, doi: 10.1007/978-981-16-2597-8_46.
N. Khan, M. Aslam, and C. H. Jun, “Design of a control chart using a modified EWMA statistic,” Quality and Reliability Engineering International, vol. 33, no. 5, pp. 1095–1104, 2017, doi: 10.1002/qre.2102.
Y. Supharakonsakun, Y. Areepong, and S. Sukparungsee, “The performance of a modified EWMA control chart for monitoring autocorrelated PM2.5 and carbon monoxide air pollution data,” PeerJ, vol. 8, 2020, Art. no. e10467, doi: 10.7717/peerj.10467.
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 & Sciences, vol. 127, no. 1, pp. 23–41, 2021, doi: 10.32604/cmes.2021. 013810.
K. Talordphop, S. Sukparungsee, and Y. Areepong, “New modified exponentially weighted moving average-moving average control chart for process monitoring,” Connection Science, vol. 34, no. 1, pp. 1981–1998, 2022, doi: 10.1080/09540091. 2022.2090513.
V. Alevizakos, K. Chatterjee, and C. Koukouvinos, “Modified EWMA and DEWMA control charts for process monitoring,” Communications in Statistics-Theory and Methods, vol. 51, no. 21, pp. 7390–7412, 2022, doi: 10.1080/ 03610926.2021.1872642.
I. Dawoud, “Modeling palestinian COVID-19 cumulative confirmed cases: A comparative study,” Infectious Disease Modelling, vol. 5, pp. 748–754, 2020, doi: 10.1016/j.idm.2020.09.001.
N. Feroze, K. Abbas, F. Noor, and A. Ali, “Analysis and forecasts for trends of COVID-19 in Pakistan using Bayesian models,” PeerJ, vol. 9, 2021, Art. no. e11537. doi: 10.7717/peerj.11537.
S. Mohan, A. K. Solanki, H. K. Taluja, and A. Singh, “Predicting the impact of the third wave of COVID-19 in India using hybrid statistical machine learning models: A time series forecasting and sentiment analysis approach,” Computers in Biology and Medicine, vol. 144, 2022, Art. no. 105354, doi: 10.1016/j.compbiomed.2022.105354.
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.
P. Phanthuna, Y. Areepong, and S. Sukparungsee, “Run length distribution for a modified EWMA scheme fitted with a stationary AR (p) model,” Communications in Statistics-Simulation and Computation, pp. 1–20, 2021, doi: 10.1080/ 03610918.2021.1958847.
K. Karoon, Y. Areepong, and S. Sukparungsee, “Exact run length evaluation on extended EWMA control chart for autoregressive process,” Intelligent Automation & Soft Computing, vol. 33, no. 2, pp. 743–759, 2022.
K. Silpakob, Y. Areepong, S. Sukparungsee, and R. Sunthornwat, “A new modified EWMA control chart for monitoring processes involving autocorrelated data,” Intelligent Automation & Soft Computing, vol. 36, no. 1, pp. 281–298, 2023.
WHO, “Coronavirus (Covid-19) Dashboard,” 2023. [Online]. Available: https://covid19.who.int/
P. Paichit and W. Peerajit, “The average run length for continuous distribution process mean shift detection on a modified EWMA control chart,” Asia-Pacific Journal of Science and Technology, vol. 27, no. 6, pp. 1–13, 2022.
S. Phanyaem, “Explicit formulas and numerical integral equation of ARL for SARX (P, r) L model based on CUSUM chart,” Mathematics and Statistics, vol. 10, no. 1, pp. 88–99, 2022, doi: 10. 13189/ms.2022.100107.
D. Bualuang and W. Peerajit, “Performance of the CUSUM control chart using approximation to ARL for long-memory fractionally integrated autoregressive process with exogenous variable,” Applied Science and Engineering Progress, vol. 16, no. 2, 2023, Art. no. 5917, doi: 10.14416/j.asep. 2022.05.003.