Robust multivariate control charts based on Birnbaum–Saunders distributions

Carolina Marchant, VICTOR ELISEO LEIVA SANCHEZ, Francisco José A. Cysneiros, Shuangzhe Liu

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Multivariate control charts are powerful and simple visual tools for monitoring the quality of a process. This multivariate monitoring is carried out by considering simultaneously several correlated quality characteristics and by determining whether these characteristics are in control or out of control. In this paper, we propose a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum–Saunders distributions and an adapted Hotelling statistic. This methodology is constructed for Phases I and II of control charts. We estimate the corresponding parameters with the maximum likelihood method and use parametric bootstrapping to obtain the distribution of the adapted Hotelling statistic. In addition, we consider the Mahalanobis distance to detect multivariate outliers and use it to assess the adequacy of the distributional assumption. A Monte Carlo simulation study is conducted to evaluate the proposed methodology and to compare it with a standard methodology. This study reports the good performance of our methodology. An illustration with real-world air quality data of Santiago, Chile, is provided. This illustration shows that the methodology is useful for alerting early episodes of extreme air pollution, thus preventing adverse effects on human health.

Original languageEnglish
Pages (from-to)182-202
Number of pages21
JournalJournal of Statistical Computation and Simulation
Issue number1
StatePublished - 2 Jan 2018


  • Average run length
  • bootstrapping
  • Hotelling statistic
  • Mahalanobis distance
  • maximum likelihood method
  • Monte Carlo simulation
  • multivariate non-normal distributions
  • R software

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