A MULTIVARIATE CONTROL CHART FOR DETECTING INCREASES IN PROCESS DISPERSION

Chia Ling Yen, Jyh-Jen Horng

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

For signalling alarms sooner when the dispersion of a multivariate process is "increased", a multivariate control chart for Phase II process monitoring is proposed as a supplementary tool to the usual monitoring schemes designed for detecting general changes in the covariance matrix. The proposed chart is constructed based on the one-sided likelihood ratio test (LRT) for testing the hypothesis that the covariance matrix of the quality characteristic vector of the current process, Sigma, is "larger" than that of the in-control process, Sigma(0), in the sense that Sigma - Sigma(0) is positive semidefinite and Sigma not equal Sigma(0). Assuming Sigma(0) is known, the LRT statistic is derived and then used to construct the control chart. A simulation study shows that the proposed control chart indeed outperforms three existing two-sided-test-based control charts under comparison in terms of the average run length. The applicability and effectiveness of the proposed control chart are demonstrated through a semiconductor example and two simulations.
Original languageEnglish
Pages (from-to)1683-1707
Number of pages25
JournalStatistica Sinica
StatePublished - Oct 2010

Keywords

  • Average run length; likelihood ratio test; multivariate process dispersion; one-sided test; two-sided test
  • ONE-SIDED TEST; PROCESS VARIABILITY; COMPONENTS; EQUALITY; CRITERIA

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