Cumulative Sum Control Charts for Monitoring Weibull-distributed Time between Events

Mohammed S. Shafae, Rebecca M. Dickinson, William H. Woodall, Jaime A. Camelio

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


The Weibull distribution can be used to effectively model many different failure mechanisms due to its inherent flexibility through the appropriate selection of a shape and a scale parameter. In this paper, we evaluate and compare the performance of three cumulative sum (CUSUM) control charts to monitor Weibull-distributed time-between-event observations. The first two methods are the Weibull CUSUM chart and the exponential CUSUM (ECUSUM) chart. The latter is considered in literature to be robust to the assumption of the exponential distribution when observations have a Weibull distribution. For the third CUSUM chart included in this study, an adjustment in the design of the ECUSUM chart is used to account for the true underlying time-between-event distribution. This adjustment allows for the adjusted ECUSUM chart to be directly comparable to the Weibull CUSUM chart. By comparing the zero-state average run length and average time to signal performance of the three charts, the ECUSUM chart is shown to be much less robust to departures from the exponential distribution than was previously claimed in the literature. We demonstrate the advantages of using one of the other two charts, which show surprisingly similar performance.

Original languageEnglish (US)
Pages (from-to)839-849
Number of pages11
JournalQuality and Reliability Engineering International
Issue number5
StatePublished - Jul 1 2015
Externally publishedYes


  • Weibull CUSUM chart
  • control chart performance
  • exponential CUSUM chart
  • time between events
  • tool life monitoring

ASJC Scopus subject areas

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


Dive into the research topics of 'Cumulative Sum Control Charts for Monitoring Weibull-distributed Time between Events'. Together they form a unique fingerprint.

Cite this