Multivariate coefficient of variation control charts in phase I of SPC

  • Saddam Akber Abbasi
  • Nurudeen A. AdegokeEmail author


Multivariate control charts are mostly available for monitoring the process mean vector or the covariance matrix. Recently, work has been done on monitoring the multivariate coefficient of variation (CV) in phase II of the statistical process control (SPC). However, no study has investigated the performance of the multivariate CV charts in phase I. The phase I procedures are more important and involve the estimation of the charts’ limits from a historical or reference dataset that represents the in-control state of the process. In real life, contaminations are mostly present in the historical samples; hence, the phase I procedures are mostly adopted to get rid of these contaminated samples. In this study, we investigate the performance of a variety of multivariate CV charts in phase I considering both diffuse symmetric and localized CV disturbance scenarios, using probability to signal as a performance measure. A real-life application, concerning carbon fiber tubing, is also provided to show the implementation of the proposed charts in phase I. The findings of this study will be useful for practitioners in their selection of an efficient phase I control chart for monitoring multivariate CV.


Coefficient of variation Multivariate control chart Phase I Probability to signal Statistical process control 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The author Saddam Akber Abbasi would like to acknowledge Qatar University for providing excellent research facilities. The author Nurudeen A. Adegoke acknowledges the support provided by the Institute of Natural and Mathematical Sciences, Massey University Albany, New Zealand, during his Ph.D. The authors also thank the editor and the referees for their constructive comments.


  1. 1.
    Montgomery D (2009) Introduction to statistical quality control, 6th ed. WileyGoogle Scholar
  2. 2.
    Jensen WA, Allison Jones-Farmer L, Champ CW, Woodall WH (2006) Effects of parameter estimation on control chart properties: a literature review. J Qual Technol 38(4)CrossRefGoogle Scholar
  3. 3.
    Zhou C, Zou C, Zhang Y, Wang Z (2007) Nonparametric control chart based on change-point model. Stat Pap 50:13–28MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Yeong WC, Khoo MBC, Teoh WL, Castagliola P (2016) A control chart for the multivariate coefficient of variation. Qual Reliab Eng Int 32(3):1213–1225CrossRefGoogle Scholar
  5. 5.
    Aerts S, Haesbroeck G, Ruwet C (2015) Multivariate coefficients of variation: comparison and influence functions. J Multivar Anal 142:183–198MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Reed GF, Lynn F, Meade BD (2002) Use of coefficient of variation in assessing variability of quantitative assays. Clin Diagn Lab Immunol 9(6):1235–1239Google Scholar
  7. 7.
    Pereira MA, Weggemans RM, Jacobs DR, Hannan PJ, Zock PL, Ordovas JM, Katan MB (2004) Within-person variation in serum lipids: implications for clinical trials. Int J Epidemiol 3333(3):534–541CrossRefGoogle Scholar
  8. 8.
    Box G (1988) Signal-to-noise ratios, performance criteria, and transformations. Technometrics 30(1):1–17MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Kang CW, Lee MANS, Hawkins DM (2007) A control chart for the coefficient of variation. J Qual Technol 39(2):151–158CrossRefGoogle Scholar
  10. 10.
    Calzada ME, Scariano SM (2013) A synthetic control chart for the coefficient of variation. J Stat Comput Simul 83(5):853–867MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Zhang J, Li Z, Chen B, Wang Z (2014) A new exponentially weighted moving average control chart for monitoring the coefficient of variation. Comput Ind Eng 78:205–212CrossRefGoogle Scholar
  12. 12.
    Castagliola P, Achouri A, Taleb H, Celano G, Psarakis S (2013) Monitoring the coefficient of variation using control charts with run rules. Qual Technol Quant Manag 10(1):75–94CrossRefGoogle Scholar
  13. 13.
    Yeong WC, Khoo MBC, Tham LK, Teoh WL, Rahim MA (2017) Monitoring the coefficient of variation using a variable sampling interval ewma chart. J Qual Technol 49(4)CrossRefGoogle Scholar
  14. 14.
    Reyment RA (1960) Studies on Nigerian Upper Cretaceous and Lower Tertiary Ostracoda. P. 1, Senonian and Maestrichtian Ostracoda. Almqvist & WiksellGoogle Scholar
  15. 15.
    Van Valen L (1974) Multivariate structural statistics in natural history. J Theor Biol 45(1):235–247CrossRefGoogle Scholar
  16. 16.
    Voinov VG, Nikulin MS (1996) Unbiased estimators and their applications: volume 2: multivariate case. Kluwer academic press, DordrechtGoogle Scholar
  17. 17.
    Albert A, Zhang L (2010) A novel definition of the multivariate coefficient of variation. Biom J 52(5):667–675MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Lim AJX, Khoo MBC, Teoh WL, Haq A (2017) Run sum chart for monitoring multivariate coefficient of variation. Comput Ind Eng 109:84–95CrossRefGoogle Scholar
  19. 19.
    Riaz M, Schoonhoven M (2011) Design and analysis of control charts for standard deviation with estimated parameters. J Qual Technol 43(4):307–333CrossRefGoogle Scholar
  20. 20.
    Adegoke NA, Smith ANH, Anderson MJ, Abbasi SA, Pawley MDM (2018) Shrinkage estimates of covariance matrices to improve the performance of multivariate cumulative sum control charts. Comput Ind Eng 117(February):207–216CrossRefGoogle Scholar
  21. 21.
    Zhang X, Liu L, Li M, Chang Y, Shang L, Dong J, Xiao L, Ao Y (2016) Improving the interfacial properties of carbon fibers/vinyl ester composites by vinyl functionalization on the carbon fiber surface. RSC Adv 6(35):29428–29436CrossRefGoogle Scholar
  22. 22.
    Deepak, Fibre Production and applications, 2017. [Online]. Available:
  23. 23.
    Santos-Fernandez E (2012) Multivariate statistical quality control using R. Springer Science & Business MediaGoogle Scholar
  24. 24.
    Santos-Fernandez E, Santos-Fernandez ME (2016) Package ‘MSQC’Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics, and PhysicsQatar UniversityDohaQatar
  2. 2.Institute of Natural and Mathematical SciencesMassey UniversityAucklandNew Zealand

Personalised recommendations