Design and Application of a Modified EWMA Control Chart for Monitoring Process Mean

Main Article Content

Yadpirun Supharakonsakun
Yupaporn Areepong

Abstract

The modified exponentially weighted moving average (modified EWMA) control chart is an improvement on the performance of the standard EWMA control chart for detecting small and abrupt shifts in the process mean. In this study, the effect of varying the constant and exponential smoothing parameters for detecting shifts in the mean of an autoregressive process with exogenous variables (ARX(p,r)) with a trend and exponentially distributed white noise on the standard and modified EWMA control chart was investigated. The performances of the two control charts were compared via their average run lengths (ARLs) computed by using explicit formulas and the numerical integrated equation (NIE) technique. A comparative study of the two ARL methods on the modified and traditional EWMA control charts shows that the modified schemes had the better detection ability at all levels of shift sizes. Finally, two examples using real datasets on gold and silver prices are given to illustrate the applicability of the proposed procedure. Our findings advocate that the modified EWMA chart is excellent for monitoring ARX(p,r) processes with exponentially distributed white noise

Article Details

How to Cite
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. https://doi.org/10.14416/j.asep.2021.06.007
Section
Research Articles

References

H. Schmidbauer and A. Rosch, “The impact of festivities on gold price expectation and volatility,” International Review of Financial Analysis, vol. 58, pp. 117–131, 2018.

Y. Qian, D. A. Ralescu, and B. Zhang, “The analysis of factors affecting global gold price,” Resources Policy, vol. 64, p. 101478, 2019.

D. G. Baur and T. K. J. McDermott, “Why is gold a safe haven,” Journal of Behavioral and Experimental Finance, vol. 10, pp. 63–71, 2016.

Y. Zhao, V. Upreti, and Y. Cai, “Stock returns, quantile autocorrelation, and volatility forecasting,” International Review of Financial Analysis, vol. 73, Jan. 2021, Art. no. 101599.

W.-J. Xue and L.-W. Zhang, “Stock return autocorrelations and predictability in the Chinese stock market-evidence from threshold quantile autoregressive models,” Economic Modelling, vol. 60, pp. 391–401, Jan. 2017.

M.-S. Pan, K. Liano, and G.-C. Huang, “Industry momentum strategies and autocorrelations in stock returns,” Journal of Empirical Finance, vol. 11, pp. 185–202, Mar. 2004.

X. Dong, S. Feng, L. Ling, and P. Song, “Dynamic autocorrelation of intraday stock returns,” Finance Research Letters, vol. 20, pp. 274–280, Feb. 2017.

M. M. Rounaghi and F. N. Zadeh, “Investigation of market efficiency and financial stability between S&P 500 and London stock exchange: Monthly and yearly forecasting of time series stock returns using ARMA model,” Physica A: Statistical Mechanics and its Application, vol. 456, pp. 10–21, Aug. 2016.

J. T. Linnainmaa, W. Torous, and J. Yae, “Reading the tea leaves: Model uncertainly, robust forecasts, and the autocorrelation of analysts’ forecast errors,” Journal of Financial Economics, vol. 122, pp. 42– 64, Jan. 2016.

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

S. W. Robert, “Control chart test based on geometric moving average,” Technometrics, vol. 1, pp. 239– 250,1959.

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

N. Khan, M. Aslam, and C. Jun, “Design of a control chart using a modified EWMA statistic,” Quality and Reliability Engineering International, vol. 41, pp. 100–114, 2017.

M. Aslam, A. Saghir, L Ahmad, and C. H. Hussain, “A control chart for COM-Poisson distribution using a modified EWMA statistic,” Journal of Statistical Computation and Simulation, vol. 87, no. 18, pp. 3491–3502, 2017.

E. T. Herdiani, G. Fandrilla, and N. Sunusi, “Modified exponential weighted moving aveage (EWMA) control chart on autocorrelation data,” Journal of Physics Conference Series, vol. 979, 2018, Art. no. 012097.

T. Noiplab and T. Mayureesawan, “Modified EWMA control chart for skewed distribution and contaminated process,” Thailand Statistician, vol. 17, pp. 16–29, 2019.

A. Saghir, A. Ahman, and M. Aslam, “Modified EWMA control chart for transformed gamma data,” Communications in Statistics-Simulation and Computation, May 2019, doi: 10.1080/03610 918.2019.1619762.

M. Aslam and S. M. Anwar, “An improved Bayesian Modified EWMA location chart and it applications in mechanical and sport industry” PLOS ONE, vol. 15, 2020, Art. no. e0229422.

Y. Supharakonsakun, Y. Areepong, and S. Sukparungsee, “The exact solution of the average run length on a modified EWMA control chart for the first-order moving-average process,” ScienceAsia, vol. 46, pp. 109–118, 2020.

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.

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.

Y. Areepong, “The exact solution of ARL on EWMA chart for nonseasonal AR model with exogenous,” Advances and Applications in Statistics, vol. 57, pp. 41–59, Jul. 2019.

W. Peerajit and Y. Areepong, “The performance of cusum control chart for monitoring process mean for autoregressive moving average with exogenous variable model,” Applied Science and Engineering Progress, 2020, Art. no. 3490, doi: 10.14416/j.asep.2020.11.007.

R. Sunthornwat and Y. Areepong, “Average run length on CUSUM control chart for seasonal and non-seasonal moving average process with exogenous variables,” Symmetry, vol. 12, no. 1, p. 173, Jan. 2020.

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, Jan. 2021.

D. C. Montgomery, Introduction to Statistical Quality Control. 6th ed., Hoboken, NJ: Wiley. Chicago, 2009, pp. 423.

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. 21, no. 1, pp. 191–204, 1991.

Wolfram Research, “WOLFRAM MATHE MATICA 8.0.,” 1998. [Online]. Available: https:// www.wolfram.com/mathematica/

M. Bildirici, F. Kay1kc1, and I. S. Onat, “BDI, Gold price and economic growth,” Procedia Economics and Finance, vol. 38, pp. 280–286, 2016.