A Control Chart for the Multivariate Coefficient of Variation

Wai Chung Yeong*, Michael Boon Chong Khoo, Wei Lin Teoh, Philippe Castagliola

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Citations (Scopus)


Existing charts in the literature usually monitor either the mean or the variance of the process. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the variance but is instead interested in monitoring the relative variability compared with the mean. This relative variability is called the coefficient of variation (CV). In the existing literature, none of the control charts that monitor the CV are applied for multivariate data. To fill this gap in research, this paper proposes a CV chart that monitors the CV for multivariate data. To the best of the authors' knowledge, this proposed chart is the first control chart for this purpose. The distributional properties of the sample CV for multivariate data and the procedures to implement the chart are presented in this paper. Formulae to compute the control limits, the average run length, the standard deviation of the run length, and the expected average run length for the case of unknown shift size are derived. From the numerical examples provided, the effects of the number of variables, the sample size, the shift size and the in-control value of the CV are studied. Finally, we demonstrate the usefulness and applicability of the proposed chart on real data.

Original languageEnglish
Pages (from-to)1213-1225
Number of pages13
JournalQuality and Reliability Engineering International
Issue number3
Publication statusPublished - 1 Apr 2016


  • average run length
  • expected average run length
  • multivariate coefficient of variation
  • relative variability
  • unknown shift size

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


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