A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

Jimoh Olawale Ajadi, Angus Wong, Tahir Mahmood*, Kevin Hung

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Multivariate charts for process dispersion detect changes in the variance-covariance matrix of a process. Most of the existing multivariate charts for monitoring the dispersion of individual observations were designed based on exponentially weighted moving average (EWMA) charting schemes. However, an alternative to the EWMA scheme is the cumulative sum (CUSUM) control chart, which has proven to be better in some cases. In the last decades, few studies have been conducted on methods based on multivariate CUSUM (MCUSUM) schemes to monitor the covariance matrix of individual observations. Consequently, we propose a new MCUSUM dispersion chart. Besides, most of the existing methods have been developed by assuming that the process parameters are known and that the process distribution is normal; these assumptions are not always true in practice. Hence, we compare the performance of the proposed chart and its counterparts based on the estimation effects under normal and non-normal distributions. The results show that the proposed chart outperforms the other charts in terms of minor shifts in the process. Similarly, the proposed chart is the most robust to the normality assumption among the compared charts. The average value of the conditional average run length was used as the performance measure. Finally, the proposed method was also implemented with a simulated dataset to support the stated proposal findings.

Original languageEnglish
Pages (from-to)834-847
Number of pages14
JournalQuality and Reliability Engineering International
Issue number2
StatePublished - Mar 2022

Bibliographical note

Publisher Copyright:
© 2021 John Wiley & Sons Ltd.


  • covariance matrix
  • estimation effects
  • individual observation
  • multivariate control chart
  • nonnormality

ASJC Scopus subject areas

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


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