Efficient Auxiliary Information Based Exponentially Weighted Moving Coefficient of Variation Control Chart using Hybrid Estimator : An Application to Monitor NPK Fertilizer

Muhammad Alifian Nuriman, Endro Setyo Cahyono


In this era, manufacturing sectors should ensure the quality of their production process and products. They must reduce the variability that occurs in their operation. Coefficient variation control charts have become important statistical Process Control (SPC) tools for monitoring processes when the process mean linear function with the standard deviation. In recent years, auxiliary information-based-CV control charts using memory type structure have been investigated to enhance the sensitivity of control charts. Auxiliary information is selected when the variable remains stable during the monitoring period. Nevertheless, the AIB statistic is constructed based on lognormal transformation, and no research investigated the memory type CV chart using estimator of AIB-CV from the combination of ratio and regression form called hybrid form. This research proposes a hybrid auxiliary information-based exponentially weighted moving coefficient of variation (Hybrid AIB-EWMCV) control chart for detecting small to moderate shifts in the CV process. The Average Run Length (ARL) simulation shows that increasing the level of correlation and sample sizes enhances the detection ability of the control chart. Also, the proposed chart performs well than existing chart. A real dataset from fertilizer manufacturing is implemented to explain the condition of the process by using a Hybrid AIB-EWMCV control chart.


Auxiliary Information; Average Run Length; Coefficient of Variation; Control Chart; NPK Fertilizer

Full Text:



C. W. Kang, M. S. Lee, Y. J. Seong, and D. M. Hawkins, "A control chart for the coefficient of variation," J. Qual. Technol., vol. 39, no. 2, pp. 151–158, 2007, doi: 10.1080/00224065.2007.11917682.

E. P. Hong, C. W. Kang, H. W. Kang, and J. W. Baik, "Development of CV Control Chart Using EWMA Technique," J. Soc. Korea Ind. Syst. Eng., vol. 31, no. 4, pp. 114–120, 2008.

E. P. Hong, H. W. Kang, and C. W. Kang, "DEWMA control chart for the coefficient of variation," in Advanced Materials Research, 2011, pp. 1682–1688. doi: 10.4028/www.scientific.net/AMR.201-203.1682.

E. P. Hong, H. W. Kang, C. W. Kang, and J. W. Baik, "CV control chart using GWMA technique," in Advanced Materials Research, 2011, pp. 247–254. doi: 10.4028/www.scientific.net/AMR.337.247.

P. Castagliola, A. Achouri, H. Taleb, G. Celano, and S. Psarakis, "Monitoring the coefficient of variation using a variable sample size control chart," Int. J. Adv. Manuf. Technol., vol. 80, no. 9–12, pp. 1561–1576, 2015, doi: 10.1007/s00170-015-6985-6.

S. M. Anwar, M. Aslam, B. Zaman, and M. Riaz, "Mixed memory control chart based on auxiliary information for simultaneously monitoring of process parameters: An application in glass field," Comput. Ind. Eng., vol. 156, 2021, doi: 10.1016/j.cie.2021.107284.

M. Noor-ul-Amin, S. Tariq, and M. Hanif, "Control charts for simultaneously monitoring of process mean and coefficient of variation with and without auxiliary information," Qual. Reliab. Eng. Int., vol. 35, no. 8, pp. 2639–2656, 2019, doi: 10.1002/qre.2546.

S. A. Abbasi, "Efficient control charts for monitoring process CV using auxiliary information," IEEE Access, vol. 8, pp. 46176–46192, 2020, doi: 10.1109/ACCESS.2020.2977833.

V. Archana and K. Aruna Rao, "Improved estimators of co-efficient of variation from bivariate normal distribution: A monte carlo comparison," Pakistan J. Stat. Oper. Res., vol. 10, no. 1, pp. 87–105, 2014, doi: 10.18187/pjsor.v10i1.433.

T. Tripathi, H. P. Singh, and L. N. Upadhyaya, "A general method of estimation and its application to the estimation of co-efficient of variation," Statist.Transition, vol. 5, no. 6, pp. 887–907, 2022.

A. Riaz, M. Noor-ul-Amin, and H. Khan, "Auxiliary information based exponentially weighted moving co-efficient of variation control chart: An application to monitor electric conductivity for water system," Commun. Stat. Case Stud. Data Anal. Appl., vol. 0, no. 0, pp. 1–20, 2020, doi: 10.1080/23737484.2020.1836533.

A. Haq and M. B. C. Khoo, "A new synthetic control chart for monitoring process mean using auxiliary information," J. Stat. Comput. Simul., vol. 86, no. 15, pp. 3068–3092, 2016, doi: 10.1080/00949655.2016.1150477.

M. Noor-ul-Amin and A. Riaz, "EWMA Control Chart for Coefficient of Variation Using Log-Normal Transformation Under Ranked Set Sampling," Iran. J. Sci. Technol. Trans. A Sci., vol. 44, no. 1, pp. 155–165, 2020, doi: 10.1007/s40995-019-00805-2.

M. A. Nuriman, M. Mashuri, and M. Ahsan, "Auxiliary information based generally weighted moving coefficient of variation (AIB-GWMCV) control chart," IOP Conf. Ser. Mater. Sci. Eng., vol. 1115, no. 1, 2021, doi: 10.1088/1757-899x/1115/1/012033.

E.S. Cahyono, M.A. Nuriman, "Auxiliary Information Based Exponentially Weighted Moving Coefficient of Variation Control Chart using Regression Estimator (AIB-EWMCVReg)," 2022. [Accepted for Publication]

Y. Bao, "Finite-sample moments of the coefficient of variation," Econom. Theory, vol. 25, no. 1, pp. 291–297, 2009, doi: 10.1017/S0266466608090555.

DOI: http://dx.doi.org/10.12962/j27213862.v5i2.14158


  • There are currently no refbacks.

Creative Commons License
Inferensi by Department of Statistics ITS is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/inferensi.

ISSN:  0216-308X

e-ISSN: 2721-3862

Analytics Made Easy - StatCounter View My Stats