Multivariate extensions to cumulative sum control charts

George Runger, Murat C. Testik

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


There are several multivariate extensions to the venerable cumulative sum (CUSUM) chart. This work provides a comparison of the advantages and disadvantages of each, as well as performance evaluations and a description of their interrelationships. A new derivation is also provided. Extensive simulation results that include initial and steady-state conditions are presented. Geometric descriptions are used, and names are proposed based on these geometric characteristics. As several of the key steps in the development of a multivariate extension to a CUSUM also appear in the construction of a two-sided CUSUM, some approaches to a two-sided CUSUM are also summarized.

Original languageEnglish (US)
Pages (from-to)587-606
Number of pages20
JournalQuality and Reliability Engineering International
Issue number6
StatePublished - Oct 2004


  • Cumulative sum
  • Exponentially weighted moving average
  • Generalized likelihood ratio
  • Multivariate process monitoring

ASJC Scopus subject areas

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


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