Percentile-based control chart design with an application to Shewhart X̅ and S2 control charts

Alireza Faraz, Erwin Saniga, Douglas Montgomery

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


We present a method to design control charts such that in-control and out-of-control run lengths are guaranteed with prespecified probabilities. We call this method the percentile-based approach to control chart design. This method is an improvement over the classical and popular statistical design approach employing constraints on in-control and out-of-control average run lengths since we can ensure with prespecified probability that the actual in-control run length exceeds a desired magnitude. Similarly, we can ensure that the out-of-control run length is less than a desired magnitude with prespecified probability. Some numerical examples illustrate the efficacy of this design method.

Original languageEnglish
Pages (from-to)116-126
Number of pages11
JournalQuality and Reliability Engineering International
Issue number1
Publication statusPublished - 1 Feb 2019


  • average run length
  • control chart
  • run length
  • statistical design
  • statistical process control


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