1. Home
  2. Vol 7, No 6 (2023)
  3. Karoon

Improving Sensitivity of the DEWMA Chart with Exact ARL Solution under the Trend AR(p) Model and Its Applications

Kotchaporn Karoon, Yupaporn Areepong

Abstract


The double exponentially weighted moving average (DEWMA) chart is a control chart that is a vital analytical tool for keeping track of the quality of a process, and the sensitivity of the control chart to the process is evaluated using the average run length (ARL). Herein, the aim of this study is to derive the explicit formula of the ARL on the DEWMA chart with the autoregressive with trend model and its residual, which is exponential white noise. This study shows that this proposed method was compared to the ARL derived using the numerical integral equation (NIE) approach, and the explicit ARL formula decreased the computing time. By changing exponential parameters that were relevant to evaluating in various circumstances, the sensitivity of AR(p) with the trend model with the DEWMA chart was investigated. These were compared with the EWMA and CUSUM charts in terms of the ARL, standard deviation run length (SDRL), and median run length (MRL). The results indicate that the DEWMA chart has the highest performance, and when it was small, the DEWMA chart had high sensitivity for detecting processes. Digital currencies are utilized to demonstrate the efficacy of the proposed method; the results are consistent with the simulated data.

 

Doi: 10.28991/ESJ-2023-07-06-03

Full Text: PDF


Keywords


Average Run Length; DEWMA Chart; EWMA Chart; Autoregressive with Trend.

References


Shewhart, W. A. (1930). Economic Quality Control of Manufactured Product1. Bell System Technical Journal, 9(2), 364–389. doi:10.1002/j.1538-7305.1930.tb00373.x.

Page, E. S. (1954). Continuous Inspection Schemes. Biometrika, 41(1/2), 100. doi:10.2307/2333009.

Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 1(3), 239. doi:10.2307/1266443.

Astill, S., Harvey, D. I., Leybourne, S. J., Taylor, A. M. R., & Zu, Y. (2023). CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility. Journal of Financial Econometrics, 21(1), 187–227. doi:10.1093/jjfinec/nbab009.

Perry, M. B. (2020). An EWMA control chart for categorical processes with applications to social network monitoring. Journal of Quality Technology, 52(2), 182–197. doi:10.1080/00224065.2019.1571343.

Abdallaha, R. A., Haridy, S., Shamsuzzaman, M., & Bashir, H. (2021). An Application of EWMA Control Chart for Monitoring Packaging Defects in Food Industry. Proceedings of the International Conference on Industrial Engineering and Operations Management, Singapore, Singapore. doi:10.46254/an11.20210410.

Alpaben, K. P., & Jyoti, D. (2011). Modified exponentially weighted moving average (EWMA) control chart for an analytical process data. Journal of Chemical Engineering and Materials Science, 2(1), 12–20. doi:10.5897/JCEMS.9000014.

Khan, N., Aslam, M., & Jun, C. H. (2017). Design of a Control Chart Using a Modified EWMA Statistic. Quality and Reliability Engineering International, 33(5), 1095–1104. doi:10.1002/qre.2102.

Naveed, M., Azam, M., Khan, N., & Aslam, M. (2018). Design of a Control Chart Using Extended EWMA Statistic. Technologies, 6(4), 108. doi:10.3390/technologies6040108.

Shamma, S. E., & Shamma, A. K. (1992). Development and Evaluation of Control Charts Using Double Exponentially Weighted Moving Averages. International Journal of Quality & Reliability Management, 9(6), 18–25. doi:10.1108/02656719210018570.

Mahmoud, M. A., & Woodall, W. H. (2010). An Evaluation of the double exponentially weighted moving average control chart. Communications in Statistics: Simulation and Computation, 39(5), 933–949. doi:10.1080/03610911003663907.

Jacobs, P. A., & Lewis, P. A. W. (1977). A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1). Advances in Applied Probability, 9(1), 87–104. doi:10.2307/1425818.

Ibazizen, M., & Fellag, H. (2003). Bayesian estimation of an AR(1) process with exponential white noise. Statistics, 37(5), 365–372. doi:10.1080/0233188031000078042.

Champ, C. W., & Rigdon, S. E. (1991). 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, 20(1), 191–204. doi:10.1080/03610919108812948.

Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of cusum run length. Biometrika, 59(3), 539–549. doi:10.1093/biomet/59.3.539.

Karoon, K., Areepong, Y., & Sukparungsee, S. (2021). Numerical integral equation methods of average run length on extended EWMA control chart for autoregressive process. Proceedings of the World Congress on Engineering (WCE 2021), 7-9 July, 2021, London, United Kingdom.

Petcharat, K., Sukparungsee, S., & Areepong, Y. (2015). Exact solution of the average run length for the cumulative sum chart for a moving average process of order q. ScienceAsia, 41(2), 141–147. doi:10.2306/scienceasia1513-1874.2015.41.141.

Sunthornwat, R., Areepong, Y., & Sukparungsee, S. (2017). Average run length of the long-memory autoregressive fractionally integrated moving average process of the exponential weighted moving average control chart. Cogent Mathematics, 4(1), 1358536. doi:10.1080/23311835.2017.1358536.

Supharakonsakun, Y. (2021). Statistical design for monitoring process mean of a modified EWMA control chart based on autocorrelated data. Walailak Journal of Science and Technology, 18(12), 19813. doi:10.48048/wjst.2021.19813.

Karoon, K., Areepong, Y., & Sukparungsee, S. (2022). Exact solution of average run length on extended EWMA control chart for the first-order autoregressive process. Thailand Statistician, 20(2), 395-411.

Karoon, K., Areepong, Y., & Sukparungsee, S. (2022). Exact Run Length Evaluation on Extended EWMA Control Chart for Autoregressive Process. Intelligent Automation and Soft Computing, 33(2), 743–759. doi:10.32604/iasc.2022.023322.

Karoon, K., Areepong, Y., & Sukparungsee, S. (2022). Exact run length evaluation on extended EWMA control chart for seasonal autoregressive process. Engineering Letters, 30(4), 1-14.

Areepong, Y., & Peerajit, W. (2022). Integral equation solutions for the average run length for monitoring shifts in the mean of a generalized seasonal ARFIMAX(P, D, Q, r)s process running on a CUSUM control chart. PLoS ONE, 17(2), 264283. doi:10.1371/journal.pone.0264283.

Phanthuna, P., & Areepong, Y. (2022). Detection Sensitivity of a Modified EWMA Control Chart with a Time Series Model with Fractionality and Integration. Emerging Science Journal, 6(5), 1134–1152. doi:10.28991/ESJ-2022-06-05-015.

Phanyaem, S. (2022). Explicit Formulas and Numerical Integral Equation of ARL for SARX(P,r)L Model Based on CUSUM Chart. Mathematics and Statistics, 10(1), 88–99. doi:10.13189/ms.2022.100107.

Peerajit, W., & Areepong, Y. (2023). Alternative to Detecting Changes in the Mean of an Autoregressive Fractionally Integrated Process with Exponential White Noise Running on the Modified EWMA Control Chart. Processes, 11(2), 503. doi:10.3390/pr11020503.

Silpakob, K., Areepong, Y., Sukparungsee, S., & Sunthornwat, R. (2023). A New Modified EWMA Control Chart for Monitoring Processes Involving Autocorrelated Data. Intelligent Automation and Soft Computing, 36(1), 281–298. doi:10.32604/iasc.2023.032487.

Silpakob, K., Areepong, Y., Sukparungsee, S., & Sunthornwat, R. (2023). Exact Average Run Length Evaluation for an ARMAX (p, q, r) Process Running on a Modified EWMA Control Chart. IAENG International Journal of Applied Mathematics, 53(1), 1-11.

Peerajit, W. (2023). Developing Average Run Length for Monitoring Changes in the Mean on the Presence of Long Memory under Seasonal Fractionally Integrated MAX Model. Mathematics and Statistics, 11(1), 34–50. doi:10.13189/ms.2023.110105.

Phanthuna, P., Areepong, Y., & Sukparungsee, S. (2021). Detection capability of the modified EWMA chart for the trend stationary AR (1) model. Thailand Statistician, 19(1), 69-80.

Petcharat, K. (2022). The Effectiveness of CUSUM Control Chart for Trend Stationary Seasonal Autocorrelated Data. Thailand Statistician, 20(2), 475–488.

Supharakonsakun, Y., & Areepong, Y. (2022). Design and Application of a Modified EWMA Control Chart for Monitoring Process Mean. Applied Science and Engineering Progress, 15(4), 5198. doi:10.14416/j.asep.2021.06.007.

Karoon, K., Areepong, Y., & Sukparungsee, S. (2023). Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart. Computer Systems Science and Engineering, 44(2), 1143–1160. doi:10.32604/csse.2023.025420.

Karoon, K., Areepong, Y., & Sukparungsee, S. (2023). On the Performance of the Extended EWMA Control Chart for Monitoring Process Mean Based on Autocorrelated Data. Applied Science and Engineering Progress, 16(4), 6599. doi:10.14416/j.asep.2023.01.004.

Almousa, M. (2020). Adomian decomposition method with modified Bernstein polynomials for solving nonlinear Fredholm and volterra integral equations. Mathematics and Statistics, 8(3), 278–285. doi:10.13189/ms.2020.080305.

Sofonea, M., Han, W., & Shillor, M. (2005). Analysis and approximation of contact problems with adhesion or damage. Chapman & Hall/CRC, New York, United States. doi:10.1201/9781420034837.

Alevizakos, V., Chatterjee, K., & Koukouvinos, C. (2021). The triple exponentially weighted moving average control chart. Quality Technology and Quantitative Management, 18(3), 326–354. doi:10.1080/16843703.2020.1809063.


Full Text: PDF

DOI: 10.28991/ESJ-2023-07-06-03

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Yupaporn Areepong