PERTANIKA JOURNAL OF SCIENCE AND TECHNOLOGY

The control charting technique is an approach to quality control and was implemented in various industries. There are many control charts, where the coefficient of variation control chart was one of the common charts and greatly used in Statistical Process Control. Since most processes are multivariate, the multivariate coefficient of variation charts has received great attention in the past few years. However, the existing multivariate coefficient of variation control charts was evaluated in terms of the average run length criterion, which may misinterpret the actual performance of the charts. This paper designs an alternative for the Shewhart multivariate coefficient of variation chart by considering the median run length and expected median run-length criteria to circumvent this problem. The research on the multivariate coefficient of variation chart is very limited in the existing literature by considering the median run length criterion. This proposed chart in this paper can minimize this research gap. The formulas and algorithms of the proposed chart are presented. The outputs of the proposed charts are shown by examining the different upward and downward process shifts. Additionally, the sample sizes, the process shifts, and the variation of the run-length distribution are investigated for their effects on the proposed chart. The findings reveal that the run-length distribution’s variation is inversely proportional to the shift size. Furthermore, it shows that the variation decreases if the shift size increases.

• Adegoke, N. A., Dawod, A., Adeoti, O. A., Sanusi, R. A. & Abbasi, S. A. (2022). Monitoring the multivariate coefficient of variation for high dimensional processes. Quality and Reliability Engineering International, 38(5), 2606-2621. https://doi.org/10.1002/qre.3094

• Alharbi, S., Raun, W. R., Arnall, D. B., & Zhang, H. (2019). Prediction of maize (Zea mays L.) population using normalized-difference vegetative index (NDVI) and coefficient of variation (CV). Journal of Plant Nutrition, 42, 673-679. https://doi.org/10.1080/01904167.2019.1568465

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

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

• Castagliola, P., Achouri, A., Taleb, H., Celano, G., & Psarakis, P. (2015). Monitoring the coefficient of variation using a variable sample size control chart. The International Journal of Advanced Manufacturing Technology, 80, 1561-1576. https://doi.org/10.1007/s00170-015-7084-4

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

• Chakraborti, S. (2007). Run-length distribution and percentiles: The Shewhart chart with unknown parameters. Quality Engineering, 19, 119-127. https://doi.org/10.1080/08982110701276653

• Chanda, S., Kanke, Y., Dalen, M., Hoy, J., & Tubana, B. (2018). Coefficient of variation from vegetarian index for sugarcane population and stalk evaluation. Agrosystems, Geosciences & Environment, 1, 1-9. https://doi.org/10.2134/age2018.07.0016

• Chew, M. H., Yeong, W. C., Talib, M. A., Lim, S. L., & Khaw, K. W. (2021). Evaluating the steady-state performance of the synthetic coefficient of variation chart. Pertanika Journal of Science and Technology, 29(3), 2149-2173. https://doi.org/10.47836/pjst.29.3.20

• Chew, X. Y., Khaw, K. W., & Yeong, W. C. (2020). The efficiency of run rules schemes for the multivariate coefficient of variation: A Markov chain approach. Journal of Applied Statistics, 47, 460-480. https://doi.org/10.1080/02664763.2019.1643296

• Chew, X. Y., Khoo, M. B. C., Khaw, K. W., Yeong, W. C., & Chong, Z. L. (2019). A proposed variable parameter control chart for monitoring the multivariate coefficient of variation. Quality and Reliability Engineering International, 35, 2442-2461. https://doi.org/10.1002/qre.2536

• Doughty, M. J., & Aakre, B. M. (2008). Further analysis of assessments of the coefficient of variation of corneal endothelial cell areas from specular microscopic images. Clinical and Experimental Optometry, 91, 438-446. https://doi.org/10.1111/j.1444-0938.2008.00281.x

• Gan, F. F. (1993). An optimal design of EWMA control charts based on median run length. Journal of Statistical Computation and Simulation, 45, 169-184. https://doi.org/10.1080/00949659308811479

• Giner-Bosch, V., Tran, K. P., Castagliola, P., & Khoo, M. B. C. (2019). An EWMA control chart for the multivariate coefficient of variation. Quality and Reliability Engineering International, 35, 1515-1541. https://doi.org/10.1002/qre.2459

• Huang, C. C., & Tang, T. (2007). Development of a new infrared device for monitoring the coefficient of variation in yarns. Journal of Applied Polymer Science, 106, 2342-2349. https://doi.org/10.1002/app.25441

• 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, 151-158. https://doi.org/10.1080/00224065.2007.11917682

• Khatun, M., Khoo, M. B. C., Lee, M. H., & Castagliola, P. (2019). One-sided control charts for monitoring the coefficient of variation in short production runs. Transactions of the Institute of Measurement and Control, 41, 1712-1728. https://doi.org/10.1177%2F0142331218789481

• Khaw, K. W., & Chew, X. Y. (2019). A re-evaluation of the run rules control charts for monitoring the coefficient of variation. Statistics, Optimization & Information Computing, 7, 716-730. https://doi.org/10.19139/soic-2310-5070-717

• Khaw, K. W., Chew, X. Y., Lee, M. H., & Yeong, W. C. (2021). An optimal adaptive variable sample size scheme for the multivariate coefficient of variation. Statistics, Optimization & Information Computing, 9, 681-693. https://doi.org/10.19139/soic-2310-5070-996

• Khaw, K. W., Chew, X. Y., Yeong, W. C., & Lim, S. L. (2019). Optimal design of the synthetic control chart for monitoring the multivariate coefficient of variation. Chemometrics and Intelligent Laboratory Systems, 186, 33-40. https://doi.org/10.1016/j.chemolab.2019.02.001

• Khaw, K. W., Khoo, M. B. C., Castagliola, P., & Rahim, M. A. (2018). New adaptive control charts for monitoring the multivariate coefficient of variation. Computers & Industrial Engineering, 126, 595-610. https://doi.org/10.1016/j.cie.2018.10.016

• Khaw, K. W., Khoo, M. B. C., Yeong, W. C., & Wu, Z. (2017). Monitoring the coefficient of variation using a variable sample size and sampling interval control chart. Communications in Statistics - Simulation and Computation, 46, 5772-5794. https://doi.org/10.1080/03610918.2016.1177074

• Khoo, M. B. C., Wong, V. H., Wu, Z., & Castagliola, P. (2012). Optimal design of the synthetic chart for the process mean based on median run length. IIE Transactions, 44, 765-779. https://doi.org/10.1080/0740817X.2011.609526

• Lee, M. H., Lim, V. Y. C., Chew, X. Y., Lau, M. F., Yakub, S., & Then, P. H. H. (2020). Design of the synthetic multivariate coefficient of variation chart based on the median run length. Advances in Mathematics: Scientific Journal, 9, 7397-7406. https://doi.org/10.37418/amsj.9.9.86

• Lim, S. L., Yeong, W. C., Khoo, M. B. C., Chong, Z. L., & Khaw, K. W. (2019). An alternative design for the variable sample size coefficient of variation chart based on the median run length and expected median run length. International Journal of Industrial Engineering: Theory, Applications, and Practice, 26, 199-220. https://doi.org/10.23055/ijietap.2019.26.2.4085

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

• 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 and Technology, 27(2), 847-866.

• Mo, Y., Ma, X., Lu, J., Shen, Y., Wang, Y., Zhang, L., Lu, W., Zhu, W., Bao, Y., & Zhou, J. (2021). Defining the target value of the coefficient of variation by continuous glucose monitoring in Chinese people with diabetes. Journal of Diabetes Investigation, 12, 1025-1034. https://dx.doi.org/10.1111%2Fjdi.13453

• Montgomery, D. C. (2013). Statistical quality control: A modern introduction. John Wiley & Sons, Inc.

• Ng, W. C., Khoo, M. B. C., Chong, Z. L., & Lee, M. H. (2022). Economic and economic-statistical designs of multivariate coefficient of variation chart. REVSTAT-Statistical Journal, 20, 117-134. https://doi.org/10.57805/revstat.v20i1.366

• Nguyen, Q. T., Tran, K. P., Heuchenne, H. L., Nguyen, T. H., & Nguyen, H. D. (2019). Variable sampling Interval Shewhart control charts for monitoring the multivariate coefficient of variation. Applied Stochastics Models in Business and Industry, 35, 1253-1268. https://doi.org/10.1002/asmb.2472

• Shriberg, L. D., Green, J. R., Campbell, T. F., Mcsweeny, J. L., & Scheer, A. R. (2003). A dianogstic marker for childhood apraxia of speech: The coefficient of variation ratio. Clinical Linguistic & Phonetics, 17, 575-595. https://doi.org/10.1080/0269920031000138141

• Teoh, W. L., Chong, J. K., Khoo, M. B. C., Castagliola, P., & Yeong, W. C. (2017). Optimal designs of the variable sample size chart based on median run length and expected median run length. Quality and Reliability Engineering International, 33, 121-134. https://doi.org/10.1002/qre.1994

• Tran, P. H., & Tran, K. P. (2016). The efficiency of CUSUM schemes for monitoring the coefficient of variation. Applied Stochastic Models in Business and Industry, 32, 870-881. https://doi.org/10.1002/asmb.2213

• Voinov, V. G., & Nikulin, M. S. (1996). Unbiased estimator and their applications, multivariate case (2nd Ed.). Kluwer Publishing.

• Wijsman, R. A. (1957). Random orthogonal transformations and their use in some classical distribution problems in multivariate analysis. The Annals of Mathematical Statistics, 28, 415-423. https://doi.org/10.1214/AOMS%2F1177706969

• Yeong, W. C., Khoo, M. B. C., Teoh, W. L., & Castagliola, P. (2016). A control chart for the multivariate coefficient of variation. Quality and Reliability Engineering International, 32, 1213-1225. https://doi.org/10.1002/qre.1828

• Yeong, W. C., Lee, P. Y., Lim, S. L., Ng, P. S., & Khaw, K. W. (2021). Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on median run length and expected median run length. PLoS ONE, 16, Article e0255366. https://doi.org/10.1371/journal.pone.0255366

• Yeong, W. C., Lim, S. L., Khoo, M. B. C., & Castagliola, P. (2018). Monitoring the coefficient of variation using a variable parameter chart. Quality Engineering, 30, 212-235. https://doi.org/10.1080/08982112.2017.1310230

• Yeong, W. C., Tan, Y. Y., Lim, S. L., Khaw, K. W., & Khoo, M. B. C. (2022). A variable sample size run sum coefficient of variation chart. Quality and Reliability Engineering International, 38, 1869-1885. https://doi.org/10.1002/qre.3057

• Zhang, J., Li, Z., Chen, B., & Wang, Z. (2014). A new exponentially weighted moving average control chart for monitoring the coefficient of variation. Computers & Industrial Engineering, 78, 205-212. https://doi.org/10.1016/j.cie.2014.09.027

• Zhou, Q., Zou, C., Wang, Z., & Jiang, W. (2012). Likelihood-based EWMA charts for monitoring Poisson count data with time-varying sample sizes. Journal of the American Statistical Association, 107, 1049-1062. https://doi.org/10.1080/01621459.2012.682811