# The Modified Double Sampling Coefficient of Variation Control Chart

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2023.55.1.4## Keywords:

coefficient of variation, control chart, double sampling, run length, molding process## Abstract

The concept of monitoring the coefficient of variation has gained significant interest in quality control, particularly in situations where the mean and standard deviation of a process are not constant. This study modified the procedure of the previous double sampling chart for monitoring the coefficient of variation, developed by Ng *et al.* in 2018. Instead of using only information from the second sample, here, information from both samples is used. The probability properties of the out-of-control signal and run length of this chart are presented. To evaluate the chart?s performance, the optimal design and a comparison with the previous double sampling control chart using average run-length criteria are described. It was found that the modified double sampling chart has better performance and is more efficient compared to the previous chart, especially when the total sample size is smaller. As a study case, the application of this chart is illustrated using real data from a molding process. This confirmed that the modified double sampling chart improved performance in detecting out-of-control signals. Thus, the modified chart is recommended to be applied in industry.

## References

Reed, G.F, Lynn, F. & Meade, B.D., Use of Coefficient of Variation in Assessing Variability of Quantitative Assays, Clin. Diagn. Lab. Immunol. 9(6), pp. 1235-1239, 2002.

Mucha, J. & Witkowski, W., The Experimental Analysis of the Double Joint Type Change Effect on the Joint Destruction Process in Uniaxial Shearing Test, Thin-Walled Structures, 66, pp. 39-49, 2013.

Gauri, S.K., Studies on the Reduction of Coefficient of Variation: A Case Study, Quality, Engineering, 17(4), pp. 633-640, 2005.

Castagliola, P., Achouri, A., Taleb H, Celano, G. & Psarakis S., Monitoring the Coefficient of Variation Using a Variable Sampling Interval Control Chart, Quality and Reliability Engineering International, 29(8), pp. 1135-1149, 2013.

Zhang, J., Li, Z., Chen, B. & Wang, Z., A New Exponentially Weighted Moving Average Control Chart for Monitoring the Coefficient of Variation, Computers & Industrial Engineering, 78, pp. 205-212, 2014.

Zhang, J., Li, Z. & Wang, Z., Control Chart for Monitoring the Coefficient of Variation with an Exponentially Weighted Moving Average Procedure, Quality and Reliability Engineering International, 34(2), pp. 188-202, 2018.

Kang, C.W., Lee, M.S., Seong, Y.J. & Hawkins, D.M., A Control Chart for the Coefficient of Variation, Journal of quality technology, 39(2), pp. 151-158, 2007.

Hong, E.P., Kang, C.W., Baek, J.W. & Kang, H.W., Development of CV Control Chart Using EWMA Technique, Journal of the society of Korea Industrial and Systems Engineering, 31(4), pp. 114-120, 2008.

Castagliola, P, Celano, G. & Psarakis, S., Monitoring the Coefficient of Variation Using EWMA Charts, Journal of Quality Technology, 43(3), pp. 249-265, 2011.

Castagliola, P., Achouri, A., Taleb, H., Celano, G. & Psarakis, S., Monitoring the Coefficient of Variation Using a Variable Sample Size Control Chart, The International Journal of Advanced Manufacturing Technology, 80, pp. 1561-1576, 2015.

Amdouni, A., Castagliola, P., Taleb, H. & Celano, G., Monitoring the Coefficient of Variation Using a Variable Sample Size Control Chart in Short Production Runs, The International Journal of Advanced Manufacturing Technology, 81, pp. 1-14, 2015.

Amdouni, A., Castagliola, P., Taleb, H. & Celano, G., A Variable Sampling Interval Shewhart Control Chart for Monitoring the Coefficient of Variation in Short Production Runs, International Journal of Production Research, 55(19), pp. 5521-5536, 2017.

Khaw, K.W, Khoo, M.B, Yeong, W.C. & Wu, Z., Monitoring the Coefficient of Variation Using a Variable Sample Size and Sampling Interval Control Chart, Communications in Statistics-Simulation and Computation 46(7), pp. 5772-5794, 2017.

Croasdale, R., Control Charts for A Double-Sampling Scheme Based on Average Production Run Lengths, International Journal of Production Research, 12(5), pp. 585-592, 1974.

Daudin, J.J., Double Sampling X? Charts, Journal of Quality Technology, 24(2), pp. 78-87, 1992.

Irianto, D. & Shinozaki, N., An Optimal Double Sampling X Control Chart, International Journal of Industrial Engineering-Applications and Practice 5(3), pp. 226-234, 1998.

He, D. & Grigoryan, A., Construction of Double Sampling S Control Charts for Agile Manufacturing, Qual. Reliab. Engng. Int., 18(4), pp. 343-355, 2002.

Costa, A., The Double Sampling Range Chart, Qual. Reliab. Engng. Int., 33(8), pp. 2739-2745, 2017.

Lee, M.H. & Khoo, M.B.C., Economic-Statistical Design of Double Sampling S Control Chart, International Journal for Quality Research, 12(2), pp. 337-362, 2018.

Ng, P.S., Khoo, M.B.C., Saha, S. & Yeong, W.C., Double sampling control charts for monitoring the coefficient of variation, In 2018 2nd International Conference on Smart Sensors and Application (ICSSA) (IEEE), pp. 93-98, 2018.

Iglewicz, B., Myers, R.H. & Howe, R.B., On the Percentage Points of the Sample Coefficient of Variation, Biometrika, 55(3), pp. 580-581, 1968.

Rozi, F., Pasaribu, U.S., Mukhaiyar, U. & Irianto, D., Modified Double Sampling Control Chart for Monitoring the Coefficient of Variation, In IOP Conf. Ser.: Mater. Sci. Eng. 598(1), 012110, 2019.