Published

2016-07-01

Nonparametric Double EWMA Control Chart for Process Monitoring

Gráfico de control EWMA doble no paramétrico del proceso de supervisión

DOI:

https://doi.org/10.15446/rce.v39n2.58914

Keywords:

ARL, Control charts, DEWMA, EQL, Nonparametric, Process location, Run length sistribution, SDRL. (en)
ARL, Gráficas de control, DEWMA, EQL, No paramétrica, Ubicación proceso, ejecutar distribución de longitud, SDRL. (es)

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Authors

  • Muhammad Riaza Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran, Saudi Arabia
  • Saddam Akber Abbasib Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran, Saudi Arabia

In monitoring process parameters, we assume normality of the quality characteristic of interest, which is an ideal assumption. In many practical situations, we may not know the distributional behavior of the data, and hence, the need arises use nonparametric techniques. In this study, a nonparametric double EWMA control chart, namely the NPDEWMA chart, is proposed to ensure efficient monitoring of the location parameter. The performance of the proposed chart is evaluated in terms of different run length properties, such as average, standard deviation and percentiles. The proposed scheme is compared with its recent existing counterparts, namely the nonparametric EWMA and the nonparametric CUSUM schemes. The performance measures used are the average run length (ARL), standard deviation of the run length (SDRL) and extra quadratic loss (EQL). We observed that the proposed chart outperforms the said existing schemes to detect shifts in the process mean level. We also provide an illustrative example for practical considerations.

 

En el seguimiento de los parámetros del proceso, asumimos normalidad
de la característica de calidad de interés que es un supuesto ideal. En muchas situaciones prácticas, no podemos conocer el comportamiento de distribución de los datos y por lo tanto, surge la necesidad de técnicas no paramétricas. En este estudio, un gráfico de control EWMA doble paramétrico, a saber, la carta NPDEWMA, se propone para una vigilancia eficaz en el parámetro de localización. El rendimiento del gráfico propuesto se evalúa en términos de propiedades diferentes de longitud de ejecución, como promedio, desviación estándar y percentiles. El esquema propuesto se compara con sus homólogos de los últimos existentes, a saber, la EWMA no paramétrico y los esquemas de CUSUM no paramétricas. Las medidas de desempeño utilizadas son la longitud promedio de carreras (ARL), la desviación estándar de la longitud de ejecución (SDRL) y pérdida cuadrática extra (EQL). Se observa que el gráfico propuesto supera a dichos regímenes existentes para detectar cambios en el proceso de nivel medio. También se proporciona un ejemplo ilustrativo para consideraciones prácticas.

https://doi.org/10.15446/rce.v39n2.58914

Nonparametric Double EWMA Control Chart for Process Monitoring

Gráfico de control EWMA doble no paramétrico del proceso de supervisión

MUHAMMAD RIAZ1, SADDAM AKBER ABBASI2

1King Fahad University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran, Saudi Arabia. Professor. Email: riazm@kfupm.edu.sa
2King Fahad University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran, Saudi Arabia. Professor. Email: saddamaa@kfupm.edu.sa

Abstract

In monitoring process parameters, we assume normality of the quality characteristic of interest, which is an ideal assumption. In many practical situations, we may not know the distributional behavior of the data, and hence, the need arises use nonparametric techniques. In this study, a nonparametric double EWMA control chart, namely the NPDEWMA chart, is proposed to ensure efficient monitoring of the location parameter. The performance of the proposed chart is evaluated in terms of different run length properties, such as average, standard deviation and percentiles. The proposed scheme is compared with its recent existing counterparts, namely the nonparametric EWMA and the nonparametric CUSUM schemes. The performance measures used are the average run length (ARL), standard deviation of the run length (SDRL) and extra quadratic loss (EQL). We observed that the proposed chart outperforms the said existing schemes to detect shifts in the process mean level. We also provide an illustrative example for practical considerations.

Key words: ARL, Control charts, DEWMA, EQL, Nonparametric, Process location, Run length sistribution, SDRL.

Resumen

En el seguimiento de los parámetros del proceso, asumimos normalidad de la característica de calidad de interés que es un supuesto ideal. En muchas situaciones prácticas, no podemos conocer el comportamiento de distribución de los datos y por lo tanto, surge la necesidad de técnicas no paramétricas. En este estudio, un gráfico de control EWMA doble paramétrico, a saber, la carta NPDEWMA, se propone para una vigilancia eficaz en el parámetro de localización. El rendimiento del gráfico propuesto se evalúa en términos de propiedades diferentes de longitud de ejecución, como promedio, desviación estándar y percentiles. El esquema propuesto se compara con sus homólogos de los últimos existentes, a saber, la EWMA no paramétrico y los esquemas de CUSUM no paramétricas. Las medidas de desempeño utilizadas son la longitud promedio de carreras (ARL), la desviación estándar de la longitud de ejecución (SDRL) y pérdida cuadrática extra (EQL). Se observa que el gráfico propuesto supera a dichos regímenes existentes para detectar cambios en el proceso de nivel medio. También se proporciona un ejemplo ilustrativo para consideraciones prácticas.

Palabras clave: ARL, gráficas de control, DEWMA, EQL, no paramétrica, ubicación proceso, ejecutar distribución de longitud, SDRL.

Texto completo disponible en PDF

References

1. Abbasi, S. A. (2010), 'On the performance of EWMA chart in the presence of two component measurement error', Quality Engineering 22(3), 199-213.

2. Abbasi, S. A. (2012), 'A new nonparametric EWMA sign control chart', Expert Systems with Applications 39(9), 1-1.

3. Abbasi, S. A. & Miller, A. (2013), 'Mdewma chart: an efficient and robust alternative to monitor process dispersion', Journal of Statistical Computation and Simulation 83(2), 247-268.

4. Ahmad, S., Lin, Z., Abbasi, S. A. & Riaz, M. (2012), 'On efficient monitoring of process dispersion using interquartile range', Open Journal of Applied Sciences 2, 39-43.

5. Ahmad, S., Riaz, M., Abbasi, S. A. & Lin, Z. (2013a), 'On monitoring process variability under double sampling scheme', International Journal of Production Economics 142(2), 388-400.

6. Ahmad, S., Riaz, M., Abbasi, S. A. & Lin, Z. (2013b), 'On efficient median control charting', Journal of the Chinese Institute of Engineers 37(3), 358-375.

7. Chakraborti, S. & Graham, M. A. (2007), Nonparametric control charts. in Encyclopedia of Statistics in Quality and Reliability, Wiley, New York.

8. Das, N. (2009), 'A comparison study of three non-parametric control charts to detect shift in location parameters', International Journal of Advanced Manufacturing Technology 41(7-8), 799-807.

9. Gan, F. F. (1994), 'An optimal design of cumulative sum control chart based on median run length', Communications in Statistics: Simulation and Computation 23(2), 485-503.

10. Graham, M. A., Chakraborti, S. & Human, S. W. (2011a), 'A nonparametric exponentially weighted moving average signed-rank chart for monitoring location', Computational Statistics and Data Analysis 55(8), 2490-2503.

11. Graham, M. A., Chakraborti, S. & Human, S. W. (2011b), 'A nonparametric EWMA sign chart for location based on individual measurements', Quality Engineering 23(2), 227-241.

12. Human, S. W., Chakraborti, S. & Smit, C. F. (2010), 'Nonparametric shewhart-type sign control charts based on runs', Communications in Statistics - Theory and Methods 39(11), 2046-2062.

13. Hwang, S. L., Lin, J. T., Liang, G. F., Yau, Y. J., Yenn, T. C. & Hsu, C. C. (2008), 'Application control chart concepts of designing a pre-alarm system in the nuclear power plant control room', Nuclear Engineering and Design 238(12), 3522-3527.

14. Khilare, S. K. & Shirke, D. T. (2010), 'A nonparametric synthetic control chart using sign statistic', Communications in Statistics - Theory and Methods 39(18), 3282-3293.

15. Khoo, M. B. C., Teh, S. Y. & Wu, Z. (2010), 'Monitoring process mean and variability with one double EWMA chart', Communications in Statistics - Theory and Methods 39(20), 3678-3694.

16. Kim, M.-J. (2010), Number of replications required in control chart Monte Carlo simulation studies, Ph.D. dissertation, University of Northern Colorado.

17. Li, S. Y., Tang, L. C. & Ng, S. H. (2010), 'Nonparametric CUSUM and EWMA control charts for detecting mean shifts', Journal of Quality Technology 42(2), 209-226.

18. Lucas, J. M. & Saccucci, M. S. (1990), 'Exponentially weighted moving average control schemes: properties and enhancements', Technometrics 32(1), 1-12.

19. Maravelakis, P., Panaretos, J. & Psarakis, S. (2005), 'An examination of the robustness to non normality of the EWMA control charts for the dispersion', Communications in Statistics-Simulation and Computation 34(4), 1069-1079.

20. Masson, P. (2007), 'Quality control techniques for routine analysis with liquid chromatography in laboratories', Journal of Chromatography 1158(1-2), 168-173.

21. Montgomery, D. C. (2009), Introduction to statistical quality control, 6 edn, Wiley, New York.

22. Page, E. S. (1954), 'Continuous inspection schemes', Biometrika 41, 100-115.

23. Pawar, V. Y. & Shirke, D. T. (2010), 'A nonparametric shewhart-type synthetic control chart', Communications in Statistics: Simulation and Computation 39(8), 1493-1505.

24. Qiu, P., Zou, C. & Wang, Z. (2010), 'Nonparametric profile monitoring by mixed effects modeling', Technometrics 52(3), 265-277.

25. Roberts, S. W. (1959), 'Control chart tests based on geometric moving averages', Technometrics 1(3), 239-250.

26. Schaffer, J. R. & Kim, M. J. (2007), 'Number of replications required in control chart monte carlo simulation studies', Communications in Statistics-Simulation and Computation 36(5), 1075-1087.

27. Shamma, S. E. & Shamma, A. K. (1992), 'Development and evaluation of control charts using double exponentially weighted moving averages', International Journal of Quality and Reliability Management 9(6), 18-25.

28. Shewhart, W. (1931), Economic Control of Quality Manufactured Product, American Society for Quality Control in 1980, New York.

29. Stoumbos, Z. & Reynolds, M. R. J. (2000), 'Robustness to non-normality and autocorrelation of individuals control charts', Journal of Statistical Computation and Simulation 66(2), 145-187.

30. Stoumbos, Z. & Sullivan, J. H. (2002), 'Robustness to non-normality of the multivariate EWMA control chart', Journal of Quality Technology 34(3), 260-276.

31. Wang, Z. & Liang, R. (2008), Discussion on applying SPC to quality management in university education, 'Proceedings of the 9th International Conference for Young Computer Scientists', ICYCS 2008, , , p. 2372-2375.

32. Woodall, W. H. (2006), 'The use of control charts in health-care and public-health surveillance', Journal of Quality Technology 38(2), 89-104.

33. Yang, S. F. & Cheng, S. W. (2011), 'A new nonparametric CUSUM sign control chart', Quality and Reliability Engineering International 27(7), 867-875.

34. Yang, S. F., Lin, J. S. & Cheng, S. W. (2011), 'A new nonparametric EWMA sign control chart', Expert Systems with Applications 38(5), 6239-6243.

35. Zhang, L. & Chen, G. (2005), 'An extended EWMA mean chart', Quality Technology & Quantitative Management 2(1), 39-52.

36. Zhang, L., Govindaraju, K., Lai, C. D. & Bebbington, M. S. (2003), 'Poisson DEWMA control chart', Communications in Statistics-Simulation and Computation 32(4), 1265-1283.

37. Zou, C. & Tsung, F. (2011), 'A multivariate sign EWMA control chart', Technometrics 53(1), 84-97.

[Recibido en noviembre de 2014. Aceptado en julio de 2015]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv39n2a02,
    AUTHOR  = {Riaz, Muhammad and Abbasi, Saddam Akber},
    TITLE   = {{Nonparametric Double EWMA Control Chart for Process Monitoring}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2016},
    volume  = {39},
    number  = {2},
    pages   = {167-184}
}

References

Abbasi, S. A. (2010), ‘On the performance of EWMA chart in the presence of two component measurement error’, Quality Engineering 22(3), 199–213.

Abbasi, S. A. (2012), ‘A new nonparametric EWMA sign control chart’, Expert Systems with Applications 39(9), 1–1.

Abbasi, S. A. & Miller, A. (2013), ‘Mdewma chart: an efficient and robust alternative to monitor process dispersion’, Journal of Statistical Computation and Simulation 83(2), 247–268.

Ahmad, S., Lin, Z., Abbasi, S. A. & Riaz, M. (2012), ‘On efficient monitoring of process dispersion using interquartile range’, Open Journal of Applied Sciences 2, 39–43.

Ahmad, S., Riaz, M., Abbasi, S. A. & Lin, Z. (2013a), ‘On efficient median control charting’, Journal of the Chinese Institute of Engineers 37(3), 358–375.

Ahmad, S., Riaz, M., Abbasi, S. A. & Lin, Z. (2013b), ‘On monitoring process variability under double sampling scheme’, International Journal of Production Economics 142(2), 388–400.

Chakraborti, S. & Graham, M. A. (2007), Nonparametric control charts. in Encyclopedia of Statistics in Quality and Reliability, Wiley, New York.

Das, N. (2009), ‘A comparison study of three non-parametric control charts to detect shift in location parameters’, International Journal of Advanced Manufacturing Technology 41(7-8), 799–807.

Gan, F. F. (1994), ‘An optimal design of cumulative sum control chart based on median run length’, Communications in Statistics: Simulation and Computation 23(2), 485–503.

Graham, M. A., Chakraborti, S. & Human, S. W. (2011a), ‘A nonparametric EWMA sign chart for location based on individual measurements’, Quality Engineering 23(2), 227–241.

Graham, M. A., Chakraborti, S. & Human, S. W. (2011b), ‘A nonparametric exponentially weighted moving average signed-rank chart for monitoring location’, Computational Statistics and Data Analysis 55(8), 2490–2503.

Human, S. W., Chakraborti, S. & Smit, C. F. (2010), ‘Nonparametric shewhart type sign control charts based on runs’, Communications in Statistics – Theory and Methods 39(11), 2046–2062.

Hwang, S. L., Lin, J. T., Liang, G. F., Yau, Y. J., Yenn, T. C. & Hsu, C. C. (2008), ‘Application control chart concepts of designing a pre-alarm system in the nuclear power plant control room’, Nuclear Engineering and Design 238(12), 3522–3527.

Khilare, S. K. & Shirke, D. T. (2010), ‘A nonparametric synthetic control chart using sign statistic’, Communications in Statistics - Theory and Methods 39(18), 3282–3293.

Khoo, M. B. C., Teh, S. Y. & Wu, Z. (2010), ‘Monitoring process mean and variability with one double EWMA chart’, Communications in Statistics - Theory and Methods 39(20), 3678–3694.

Kim, M.-J. (2010), Number of replications required in control chart Monte Carlo simulation studies, Ph.d. dissertation, University of Northern Colorado.

Li, S. Y., Tang, L. C. & Ng, S. H. (2010), ‘Nonparametric CUSUM and EWMA control charts for detecting mean shifts’, Journal of Quality Technology 42(2), 209–226.

Lucas, J. M. & Saccucci, M. S. (1990), ‘Exponentially weighted moving average control schemes: Properties and enhancements’, Technometrics 32(1), 1–12.

Maravelakis, P., Panaretos, J. & Psarakis, S. (2005), ‘An examination of the robustness to non normality of the EWMA control charts for the dispersion’, Communications in Statistics-Simulation and Computation 34(4), 1069–1079.

Masson, P. (2007), ‘Quality control techniques for routine analysis with liquid chromatography in laboratories’, Journal of Chromatography 1158(1-2), 168–173.

Montgomery, D. C. (2009), Introduction to statistical quality control, 6 edn, Wiley, New York.

Page, E. S. (1954), ‘Continuous inspection schemes’, Biometrika 41, 100–115.

Pawar, V. Y. & Shirke, D. T. (2010), ‘A nonparametric shewhart-type synthetic control chart’, Communications in Statistics: Simulation and Computation 39(8), 1493–1505.

Qiu, P., Zou, C. & Wang, Z. (2010), ‘Nonparametric profile monitoring by mixed effects modeling’, Technometrics 52(3), 265–277.

Roberts, S. W. (1959), ‘Control chart tests based on geometric moving averages’, Technometrics 1(3), 239–250.

Schaffer, J. R. & Kim, M. J. (2007), ‘Number of replications required in control chart monte carlo simulation studies’, Communications in Statistics-Simulation and Computation 36(5), 1075–1087.

Shamma, S. E. & Shamma, A. K. (1992), ‘Development and evaluation of control charts using double exponentially weighted moving averages’, International Journal of Quality and Reliability Management 9(6), 18–25.

Shewhart, W. (1931), Economic Control of Quality Manufactured Product, American Society for Quality Control in 1980, New York.

Stoumbos, Z. & Reynolds, M. R. J. (2000), ‘Robustness to non-normality and autocorrelation of individuals control charts’, Journal of Statistical Computation and Simulation 66(2), 145–187.

Stoumbos, Z. & Sullivan, J. H. (2002), ‘Robustness to non-normality of the multivariate EWMA control chart’, Journal of Quality Technology 34(3), 260–276.

Wang, Z. & Liang, R. (2008), Discussion on applying SPC to quality management in university education, in ‘Proceedings of the 9th International Conference for Young Computer Scientists’, ICYCS 2008, pp. 2372–2375.

Woodall, W. H. (2006), ‘The use of control charts in health-care and public-health surveillance’, Journal of Quality Technology 38(2), 89–104.

Yang, S. F. & Cheng, S. W. (2011), ‘A new nonparametric CUSUM sign control chart’, Quality and Reliability Engineering International 27(7), 867–875.

Yang, S. F., Lin, J. S. & Cheng, S. W. (2011), ‘A new nonparametric EWMA sign control chart’, Expert Systems with Applications 38(5), 6239–6243.

Zhang, L. & Chen, G. (2005), ‘An extended EWMA mean chart’, Quality Technology & Quantitative Management 2(1), 39–52.

Zhang, L., Govindaraju, K., Lai, C. D. & Bebbington, M. S. (2003), ‘Poisson DEWMA control chart’, Communications in Statistics-Simulation and Computation 32(4), 1265–1283.

Zou, C. & Tsung, F. (2011), ‘A multivariate sign EWMA control chart’, Technometrics 53(1), 84–97.

How to Cite

APA

Riaza, M. and Abbasib, S. A. (2016). Nonparametric Double EWMA Control Chart for Process Monitoring. Revista Colombiana de Estadística, 39(2), 167–184. https://doi.org/10.15446/rce.v39n2.58914

ACM

[1]
Riaza, M. and Abbasib, S.A. 2016. Nonparametric Double EWMA Control Chart for Process Monitoring. Revista Colombiana de Estadística. 39, 2 (Jul. 2016), 167–184. DOI:https://doi.org/10.15446/rce.v39n2.58914.

ACS

(1)
Riaza, M.; Abbasib, S. A. Nonparametric Double EWMA Control Chart for Process Monitoring. Rev. colomb. estad. 2016, 39, 167-184.

ABNT

RIAZA, M.; ABBASIB, S. A. Nonparametric Double EWMA Control Chart for Process Monitoring. Revista Colombiana de Estadística, [S. l.], v. 39, n. 2, p. 167–184, 2016. DOI: 10.15446/rce.v39n2.58914. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/58914. Acesso em: 4 aug. 2024.

Chicago

Riaza, Muhammad, and Saddam Akber Abbasib. 2016. “Nonparametric Double EWMA Control Chart for Process Monitoring”. Revista Colombiana De Estadística 39 (2):167-84. https://doi.org/10.15446/rce.v39n2.58914.

Harvard

Riaza, M. and Abbasib, S. A. (2016) “Nonparametric Double EWMA Control Chart for Process Monitoring”, Revista Colombiana de Estadística, 39(2), pp. 167–184. doi: 10.15446/rce.v39n2.58914.

IEEE

[1]
M. Riaza and S. A. Abbasib, “Nonparametric Double EWMA Control Chart for Process Monitoring”, Rev. colomb. estad., vol. 39, no. 2, pp. 167–184, Jul. 2016.

MLA

Riaza, M., and S. A. Abbasib. “Nonparametric Double EWMA Control Chart for Process Monitoring”. Revista Colombiana de Estadística, vol. 39, no. 2, July 2016, pp. 167-84, doi:10.15446/rce.v39n2.58914.

Turabian

Riaza, Muhammad, and Saddam Akber Abbasib. “Nonparametric Double EWMA Control Chart for Process Monitoring”. Revista Colombiana de Estadística 39, no. 2 (July 1, 2016): 167–184. Accessed August 4, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/58914.

Vancouver

1.
Riaza M, Abbasib SA. Nonparametric Double EWMA Control Chart for Process Monitoring. Rev. colomb. estad. [Internet]. 2016 Jul. 1 [cited 2024 Aug. 4];39(2):167-84. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/58914

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