Abstract—The double sampling (DS) X 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 X chart based on MRL is proposed. New optimal parameters are provided for selected in-control median run lengths, ∈ 0 MRL {250, 500} and in-control average sample sizes, ∈ 0 ASS {3, 5, 7, 9}. These optimal parameters facilitate the implementation of the DS X chart in practice.
Index Terms—Average sample size, double sampling Xchart, median run length, optimization
The authors are with the School of Mathematical Sciences, Universiti Sains Malaysia, and 11800 Penang, Malaysia (e-mail:weilin.teoh@gmail.com, mkbc@usm.my).
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Cite: Wei Lin Teoh and Michael B. C. Khoo, "Optimal Design of the Double Sampling X Chart Based on Median Run Length," International Journal of Chemical Engineering and Applications vol. 3, no. 5, pp. 303-306, 2012.
