Performance of EWMA Chart for Trend Autoregressive Model with Exponential White Noise
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Published:
Aug 31, 2017
Keywords:
ARL autoregressive model EWMA chart integral equation
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Abstract
In this paper, we propose an explicit formula of the performance for Exponentially Weighted Moving Average (EWMA) chart by using the Fredholm integral equation of the second kind and the data are described by trend Exponential Autoregressive order p (EAR(p)) model. The performance of the chart is usually measured by the Average Run Length (ARL). The solution is compared with numerical approximations and we found that the computational time of the explicit formula take approximately 1 second while the numerical computations were approximately 10 minutes.
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How to Cite
Suriyakat, W. (2017). Performance of EWMA Chart for Trend Autoregressive Model with Exponential White Noise. Science, Engineering and Health Studies, 11(2), 16–22. https://doi.org/10.14456/sustj.2017.6
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Research Articles
References
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Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of CUSUM run length. Biometrika, 59(3), 539-549.
Busaba, J., Sukparungsee, S., Areepong, Y., & Mititelu, G. (2012). Analysis of average run length for CUSUM procedure with negative exponential data. Chiang Mai Journal of Science, 39(2), 200-208.
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 Computation, 32(2), 591-604.
Calzada, M. E., & Scariano, S. M. (2004). Average run length computations for the three-way chart. Communications in Statistics-Simulation and Computation, 33(2), 505-524.
Chang, Y. M., & Wu, T. L. (2011). On average run lengths of control charts for autocorrelated processes. Methodology and Computing in Applied Probability, 13(2), 419-431.
Crowder, S. V. (1987). A simple method for studying run–length distributions of exponentially weighted moving average charts. Technometrics, 29(4), 401-407.
Haq, A., Brown, J., & Moltchanova, E. (2015). New exponentially weighted moving average control charts for monitoring process mean and process dispersion. Quality and Reliability Engineering International, 31(5), 877-901.
Huang, W., Shu, L., & Jiang, W. (2012). Evaluation of exponentially weighted moving variance control chart subject to linear drifts. Computational Statistics & Data Analysis, 56(12), 4278-4289.
Mititelu, G., Areepong, Y., Sukparungsee, S., & Novikov, A. (2010). Explicit analytical solutions for the average run length of CUSUM and EWMA charts.East-West Journal of Mathematics, 253-265.
Morais, M. C., Okhrin, Y., & Schmid, W. (2015). Quality surveillance with EWMA control charts based on exact control limits. Statistical Papers, 56(3), 863-885.
Petcharat, K., Areepong, Y., Sukparungsee, S., & Mititelu, G. (2014). Exact solution for average run length of CUSUM charts for MA(1) Process. Chiang Mai Journal of Science, 41, 1449-1456.
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, 141-147.
Rabyk, L., & Schmid, W. (2016). EWMA control charts for detecting changes in the mean of a long-memory process. Metrika, 79(3), 267-301.
Riaz, M. & Ahmad, S. (2016). On designing a new Tukey-EWMA control chart for process monitoring. The International Journal of Advanced Manufacturing Technology, 82(1-4), 1-23.
Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 20(1), 239-250.
Saleh, N. A., Mahmoud, M. A., & Abdel-Salam, A. S. G. (2013). The performance of the adaptive exponentially weighted moving average control chart with estimated parameters. Quality and Reliability Engineering International, 29(4), 595-606.
Suriyakat, W., Areepong, Y., Sukparungsee, S., & Mititelu, G. (2012). On EWMA procedure for AR (1) observations with exponential white noise. International Journal of Pure and Applied Mathematics, 77, 73-83.
Zhang, M., Nie, G., He, Z., & Hou, X. (2014). The Poisson INAR(1) one-sided EWMA chart with estimated parameters. International Journal of Production Research, 52(18), 5415-5431.
Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of CUSUM run length. Biometrika, 59(3), 539-549.
Busaba, J., Sukparungsee, S., Areepong, Y., & Mititelu, G. (2012). Analysis of average run length for CUSUM procedure with negative exponential data. Chiang Mai Journal of Science, 39(2), 200-208.
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 Computation, 32(2), 591-604.
Calzada, M. E., & Scariano, S. M. (2004). Average run length computations for the three-way chart. Communications in Statistics-Simulation and Computation, 33(2), 505-524.
Chang, Y. M., & Wu, T. L. (2011). On average run lengths of control charts for autocorrelated processes. Methodology and Computing in Applied Probability, 13(2), 419-431.
Crowder, S. V. (1987). A simple method for studying run–length distributions of exponentially weighted moving average charts. Technometrics, 29(4), 401-407.
Haq, A., Brown, J., & Moltchanova, E. (2015). New exponentially weighted moving average control charts for monitoring process mean and process dispersion. Quality and Reliability Engineering International, 31(5), 877-901.
Huang, W., Shu, L., & Jiang, W. (2012). Evaluation of exponentially weighted moving variance control chart subject to linear drifts. Computational Statistics & Data Analysis, 56(12), 4278-4289.
Mititelu, G., Areepong, Y., Sukparungsee, S., & Novikov, A. (2010). Explicit analytical solutions for the average run length of CUSUM and EWMA charts.East-West Journal of Mathematics, 253-265.
Morais, M. C., Okhrin, Y., & Schmid, W. (2015). Quality surveillance with EWMA control charts based on exact control limits. Statistical Papers, 56(3), 863-885.
Petcharat, K., Areepong, Y., Sukparungsee, S., & Mititelu, G. (2014). Exact solution for average run length of CUSUM charts for MA(1) Process. Chiang Mai Journal of Science, 41, 1449-1456.
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, 141-147.
Rabyk, L., & Schmid, W. (2016). EWMA control charts for detecting changes in the mean of a long-memory process. Metrika, 79(3), 267-301.
Riaz, M. & Ahmad, S. (2016). On designing a new Tukey-EWMA control chart for process monitoring. The International Journal of Advanced Manufacturing Technology, 82(1-4), 1-23.
Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 20(1), 239-250.
Saleh, N. A., Mahmoud, M. A., & Abdel-Salam, A. S. G. (2013). The performance of the adaptive exponentially weighted moving average control chart with estimated parameters. Quality and Reliability Engineering International, 29(4), 595-606.
Suriyakat, W., Areepong, Y., Sukparungsee, S., & Mititelu, G. (2012). On EWMA procedure for AR (1) observations with exponential white noise. International Journal of Pure and Applied Mathematics, 77, 73-83.
Zhang, M., Nie, G., He, Z., & Hou, X. (2014). The Poisson INAR(1) one-sided EWMA chart with estimated parameters. International Journal of Production Research, 52(18), 5415-5431.