A nonparametric multivariate cumulative sum procedure for detecting shifts in all directions

Peihua Qiu, Douglas Hawkins

Research output: Contribution to journalArticlepeer-review

96 Scopus citations

Abstract

The fairly limited range of tools for multivariate statistical process control generally rests on the assumption that the data vectors follow a multivariate normal distribution - an assumption that is rarely satisfied. We discuss detecting possible shifts in the mean vector of a multivariate measurement of a statistical process when the multivariate distribution of the measurement is non-Gaussian. A nonparametric cumulative sum procedure is suggested which is based both on the order information among the measurement components and on the order information between the measurement components and their in-control means. It is shown that this procedure is effective in detecting a wide range of possible shifts. Several numerical examples are presented to evaluate its performance. This procedure is also applied to a data set from an aluminium smelter.

Original languageEnglish (US)
Pages (from-to)151-164
Number of pages14
JournalJournal of the Royal Statistical Society Series D: The Statistician
Volume52
Issue number2
DOIs
StatePublished - Oct 27 2003

Keywords

  • Antiranks
  • Cumulative sum
  • Distribution-free procedures
  • Order statistics
  • Robustness
  • Statistical process control

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