Optimal design of the double sampling X chart based on median run length

Wei Lin Teoh, Michael B. C. Khoo

Research output: Contribution to journalArticlepeer-review


The double sampling (DS) Xbar chart is effective in detecting small to moderate process mean shifts and reducing the sample size. The average run length (ARL) is an intuitively appealing and widely used optimization criterion in the design
of a control chart. Nevertheless, the skewness of the run length distribution changes with the size of the process mean shift; thus, ARL is not necessarily a good representative of the run length distribution. In such a case, the median run length (MRL) provides a more reliable interpretation, for the in-control and
out-of-control performances of a control chart. In this paper, an optimal design of the DS Xbar chart based on MRL is proposed. New optimal parameters are provided for selected in-control median run lengths, MRL0 ∈ {250, 500} and in-control average sample sizes, ASS0 ∈ {3, 5, 7, 9}. These optimal parameters facilitate the implementation of the DS Xbar chart in practice.
Original languageEnglish
Pages (from-to)303-306
JournalInternational Journal of Chemical Engineering and Applications
Issue number5
Publication statusPublished - Oct 2012


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