Identifying the time of a step-change with χ2 control charts

Gunabushanam Nedumaran, Joseph J. Pignatiello, James A. Calvin

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


If a control chart signals a change in the process parameter, identifying the time of change will substantially help the signal diagnostics procedure because it simplifies the search for special causes. In this article, we propose a maximum likelihood estimator for the time of a step-change in a multivariate process mean when the observations follow a multivariate Normal distribution. We describe how this estimator can be used to identify the change point when a multivariate χ2 control chart signals a change in the process mean. We illustrate the use of our proposed estimator with an example. We assess the performance of the estimator through computer simulation experiments. The results show that our proposed estimator performs effectively and equally well for all process dimensions and shift magnitudes considered. Thus, the estimator provides process engineers with an accurate and useful estimate of the actual time of the change in the process mean.

Original languageEnglish (US)
Pages (from-to)153-159
Number of pages7
JournalQuality Engineering
Issue number2
StatePublished - 2000
Externally publishedYes


  • Change-point estimation
  • Hotelling's T
  • Maximum likelihood estimation
  • Monte Carlo simulation
  • Multivariate process
  • Process improvement
  • Special-cause identification
  • Statistical process control
  • T control charts
  • χ control charts

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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