A Change Point Model for a Shift in Variance

Douglas M. Hawkins, K. D. Zamba

Research output: Contribution to journalArticlepeer-review

94 Scopus citations

Abstract

A control chart for detecting shifts in the variance of a process is developed for the case where the nominal value of the variance is unknown. As our approach does not require that the in-control variance be known a priori, it avoids the need for a lengthy Phase I data-gathering step before charting can begin. The method is a variance-change-point model, based on the likelihood ratio test for a change in variance with the conventional Bartlett correction, adapted for repeated sequential use. The chart may be used alone in settings where one wishes to monitor one-degree-of-freedom chi-squared variates for departure from control; or it may be used together with a parallel change-point methodology for the mean to monitor process data for shifts in mean and/or variance. In both the solo use and as the scale portion of a combined scheme for monitoring changes in mean and/or variance, the approach has good performance across the range of possible shifts.

Original languageEnglish (US)
Pages (from-to)21-31
Number of pages11
JournalJournal of Quality Technology
Volume37
Issue number1
DOIs
StatePublished - Jan 2005

Keywords

  • Average Run Length
  • CUSUM
  • Change Point
  • Control Chart
  • EWMA
  • Likelihood Ratio
  • Phase I
  • Phase II
  • Shewhart

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