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Evaluating the Steady-state Performance of the Synthetic Coefficient of Variation Chart

Ming Hui Chew, Wai Chung Yeong, Muzalwana Abdul Talib, Sok Li Lim and Khai Wah Khaw

Pertanika Journal of Social Science and Humanities, Volume 29, Issue 3, July 2021

DOI: https://doi.org/10.47836/pjst.29.3.20

Keywords: Coefficient of variation; control chart, exponentially weighted moving average, run rules, Shewhart, steady-state, synthetic chart, zero-state

Published on: 31 July 2021

The synthetic coefficient of variation (CV) chart is attractive to practitioners as it allows for a second point to fall outside the control limits before deciding whether the process is out-of-control. The existing synthetic CV chart is designed with a head-start feature, which shows an advantage under the zero-state assumption where shifts happen immediately after process monitoring has started. However, this assumption may not be valid as shifts may happen quite some time after process monitoring has started. This is called the steady-state condition. This paper evaluates the performance of the chart under the steady-state condition. It is shown that the steady-state out-of-control average run length (ARL1) is substantially larger than the zero-state ARL1, hence larger number of samples are needed to detect the out-of-control condition. From the comparison with other CV charts, the steady-state synthetic CV chart does not show better performance, especially for small sample sizes and shift sizes. Hence, the synthetic CV chart is not recommended to be adopted under the steady-state condition, and its good performance is only applicable under the zero-state assumption. The results of this paper enable practitioners to be aware that the performance of the synthetic CV chart may be inferior under actual application (when shifts do not happen at the beginning of process monitoring) compared to its zero-state performance.

  • Calzada, M. E., & Scariano, S. M. (2013). A synthetic control chart for the coefficient of variation. Journal of Statistical Computation and Simulation, 83(5), 853-867. https://doi.org/10.1080/00949655.2011.639772

  • Castagliola, P., Achouri, A., Taleb, H., Celano, G., & Psarakis, S. (2013). Monitoring the coefficient of variation using control charts with run rules. Quality Technology and Quantitative Management, 10(1), 75-94. https://doi.org/10.1080/16843703.2013.11673309

  • Castagliola, P., Celano, G., & Psarakis, S. (2011). Monitoring the coefficient of variation using EWMA charts. Journal of Quality Technology, 43(3), 249-265. https://doi.org/10.1080/00224065.2011.11917861

  • Curto, J. D., & Pinto, J. C. (2009). The coefficient of variation asymptotic distribution in the case of non-iid random variables. Journal of Applied Statistics, 36(1), 21-32. https://doi.org/10.1080/02664760802382491

  • Davis, R. B., & Woodall, W. H. (2002). Evaluating and improving the synthetic control chart. Journal of Quality Technology, 34(2), 200-208. https://doi.org/10.1080/00224065.2002.11980146

  • Kang, C. W., Lee, M. S., Seong, Y. J., & Hawkins, D. M. (2007). A control chart for the coefficient of variation. Journal of Quality Technology, 39(2), 151-158. https://doi.org/10.1080/00224065.2007.11917682

  • Khan, Z., Razali, R. B., Daud, H., Nor, N. M., & Fotuhi-Firuzabad, M. (2017). The control chart technique for the detection of the problem of bad data in state estimation power system. Pertanika Journal of Science & Technology, 25(3), 825-834.

  • Kinat, S., Amin, M., & Mahmood, T. (2020). GLM-based control charts for the inverse Gaussian distributed response variable. Quality and Reliability Engineering International, 36(2), 765-783. https://doi.org/10.1002/qre.2603

  • Knoth, S. (2016). The case against the use of the synthetic control charts. Journal of Quality Technology, 48(2), 178-195. https://doi.org/10.1080/00224065.2016.11918158

  • Machado, M. A. G., & Costa, A. F. B. (2014). Some comments regarding the synthetic chart. Communications in Statistics - Theory and Methods, 43(14), 2897-2906. https://doi.org/10.1080/03610926.2012.683128

  • Mahmood, T., & Abbasi, S. A. (2021). Efficient monitoring of coefficient of variation with an application to chemical reactor process. Quality and Reliability Engineering International, 37(3), 1135-1149. https://doi.org/10.1002/qre.2785

  • Marchant, C., Leiva, V., Cysneiros, F. J. A., & Liu, S. (2018). Robust multivariate control charts based on Birnbaum-Saunders distributions. Journal of Statistical Computation and Simulation, 88(1), 182-202. https://doi.org/10.1080/00949655.2017.1381699

  • Mim, F. N., Saha, S., Khoo, M. B. C., & Khatun, M. (2019). A side-sensitive modified group runs control chart with auxiliary information to detect process mean shifts. Pertanika Journal of Science & Technology, 27(2), 847-866.

  • Montgomery, D. C. (2019). Introduction to statistical quality control. John Wiley and Sons Inc.

  • Pang, W. K., Yu, B. W., Troutt, M. D., & Shui, H. H. (2008). A simulation-based approach to the study of coefficient of variation of dividend yields. European Journal of Operational Research, 189(2), 559-569. https://doi.org/10.1016/j.ejor.2007.05.032

  • Rakitzis, A. C., Chakraborti, S., Shongwe, S. C., Graham, M. A., & Khoo, M. B. C. (2019). An overview of synthetic-type control charts: Techniques and methodology. Quality and Reliability Engineering International, 35(7), 2081-2096. https://doi.org/10.1002/qre.2491

  • Shongwe, S. C., & Graham, M. A. (2017). A letter to the editor about “Machado, MAG and Costa AFB (2014), some comments regarding the synthetic chart. Communications in Statistics---Theory and Methods, 43 (14), 2897–2906”. Communications in Statistics - Theory and Methods, 46(21), 10476-10480. https://doi.org/10.1080/03610926.2016.1236958

  • Shongwe, S. C., & Graham, M. A. (2019). Some theoretical comments regarding the run-length properties of the synthetic and runs-rules X¯ monitoring schemes–part 2: Steady-state. Quality Technology & Quantitative Management, 16(2), 190-199. https://doi.org/10.1080/16843703.2017.1389141

  • Teoh, W. L., Khoo, M. B. C., Yeong, W. C., & Teh, S. Y. (2016). A comparison between the performances of synthetic and EWMA charts for monitoring the coefficient of variation. Journal of Scientific Research and Development, 3(1), 16-20.

  • Wu, Z., & Spedding, T. A. (2000). A synthetic control chart for detecting small shifts in the process mean. Journal of Quality Technology, 32(1), 32-38. https://doi.org/10.1080/00224065.2000.11979969

  • Wu, Z., Ou, Y., Castagliola, P., & Khoo, M. B. C. (2010). A combined synthetic & X chart for monitoring the process mean. International Journal of Production Research, 48(24), 7423-7436. https://doi.org/10.1080/00207540903496681

  • Yeong, W. C., Khoo, M. B. C., Tham, L. K., Teoh, W. L., & Rahim, M. A. (2017). Monitoring the coefficient of variation using a variable sampling interval EWMA chart. Journal of Quality Technology, 49(4), 380-401. https://doi.org/10.1080/00224065.2017.11918004

  • Yeong, W. C., Lim, S. L., Khoo, M. B. C., Chuah, M. E., & Lim, A. J. X. (2018). The economic and economic-statistical designs of the synthetic chart for the coefficient of variation. Journal of Testing and Evaluation, 46(3), 1175-1195. https://doi.org/10.1520/JTE20160500

  • You, H. W. (2018). Design of the side sensitive group runs chart with estimated parameters based on expected average run length. Pertanika Journal of Science & Technology, 26(3), 847-866.

  • Zhang, J., Li, Z., & Wang, Z. (2018). Control chart for monitoring the coefficient of variation with an exponentially weighted moving average procedure. Quality and Reliability Engineering International, 34(2), 188-202. https://doi.org/10.1002/qre.2247

ISSN 0128-7702

e-ISSN 2231-8534

Article ID

JST-2353-2020

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