Robustness of the time between events CUSUM

Connie M. Borror, J. Bert Keats, Douglas Montgomery

Research output: Contribution to journalArticlepeer-review

82 Scopus citations


Many companies have set Parts per Million (PPM) or Parts per Million Opportunities (PPMO) goals in their quest for continuous improvement. The time-between-events (TBE) CUSUM has been suggested for monitoring the number of good units or the number of opportunities that occurred between discoveries of consecutive bad units. We focus on the robustness of the TBE CUSUM. Robustness, in this case, refers to sensitivity of the procedure to make the proper decisions regarding a shift in the mean defect rate when, in fact, the time between events is not exponential. We examine and report average run lengths (ARLs) under both a Weibull and a lognormal time between events distribution. Our results indicate that the TBE CUSUM is extremely robust for a wide variety of parameter values for both the Weibull and lognormal distributions. The implications of these results in practice imply that users of the TBE CUSUM procedure need not be concerned about departures from the exponential TBE distribution. Practical implementation of the TBE CUSUM procedure is also discussed.

Original languageEnglish (US)
Pages (from-to)3435-3444
Number of pages10
JournalInternational Journal of Production Research
Issue number15
StatePublished - Oct 15 2003

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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