Modified Multivariate Cumulative Sum Control Chart Based On Robust Estimators

  • Nazihah Mohd Ali Mathematics & Statistics Department, UPM
  • A.S. Razalee Department of Mathematics and Statistics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor
  • N. Ali Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Malaysia
  • N. A. A. Rahmin Department of Mathematics and Statistics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor


Multivariate cumulative sum (MCUSUM) control charts are one of the popular tools for monitoring multivariate statistical process control aside from the Hotelling  and the multivariate exponentially weighted moving average (MEWMA) control chart. However, these charts are easily affected by outliers or shifts in the dataset. To overcome the problem, this study will integrate several robust approaches to the classical MCUSUM control chart. These approaches used robust location and scale estimator to substitute the usual mean and covariance matrix, respectively into the classical MCUSUM. The two robust location estimators used are the modified one-step M estimator (MOM) and Hodges Lehmann estimator (HL). Then, a scale estimator named Madn was introduced and functioned accordingly to the robust location estimators. Altogether, two robust MCUSUM control charts were proposed. The performance of each control chart was monitored based on their probability in detecting mean shifts. Various conditions were created to investigate the performance of proposed and classical control chart, namely the subgroup size  number of quality characteristics  and the level mean shifts  The simulation results show that all the proposed charts are able to outperform the classical chart in term of their probability of detecting mean shift. This shows that the proposed robust MCUSUM charts can be used as an alternative if outliers or shifts happen to present in the dataset.


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How to Cite
MOHD ALI, Nazihah et al. Modified Multivariate Cumulative Sum Control Chart Based On Robust Estimators. Menemui Matematik (Discovering Mathematics), [S.l.], v. 45, n. 2, p. 247-258, nov. 2023. ISSN 0126-9003. Available at: <>. Date accessed: 26 july 2024.

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