The np Chart with Guaranteed In-control Average Run Lengths

Alireza Faraz, Cedric Heuchenne, Erwin Saniga

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We evaluate the in-control performance of the np-control chart with estimated parameter conditional on the Phase I sample. We then apply the bootstrap method to adjust the control chart limits to guarantee the desired in-control average run length (ARL0) value in the monitoring stage. The adjusted limits ensure that the ARL0 would take a value greater than the desired value (say, B) with a certain specified probability, that is, Pr(ARL0 > B) = 1 − ρ. The results indicate that adjusting control limits is not always necessary. We present a method to design control charts such that in control and out of control run lengths are guaranteed with pre specified probabilities. This method is an improvement of the classical statistical design approach employing constraints on in control and out of control ARL because, with this approach, there is a substantial probability that the actual run length in control may be too small. In addition, using the ARL approach may result in an actual out of control run length that is too large. Some numerical examples illustrate the efficacy of this design method.

Original languageEnglish
Pages (from-to)1057-1066
Number of pages10
JournalQuality and Reliability Engineering International
Issue number5
Publication statusPublished - Jul 2017


  • average run length (ARL)
  • effect of estimation error
  • np-charts, Bootstrap
  • the average of ARL (AARL)
  • the standard deviation of ARL (SDARL)


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