THE REVISED M-OF-K RUNS RULES BASED ON MEDIAN RUN LENGTH
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Date
2011-05
Authors
LOW, CHUN KIT
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Abstract
Runs rules are used to increase the sensitivity of the Shewhart X control chart in
detecting small and moderate process mean shifts. Most of the X charts incorporating
runs rules are designed based on the average run length (ARL) as a criterion to be
minimized. It is known that the shape of the run length distribution changes according to
the magnitude of the shift in the process mean, i.e. ranging from highly skewed when the
process is in-control to approximately symmetric when the shift is large. Since the shape
of the run length distribution changes with the magnitude of the shift in the mean, the
median run length (MRL) provides a more meaningful explanation about the in-control
and out-of-control performances of a control chart. In this thesis, the design of the revised
m-of-k (R - mlk) runs rules based on MRL is proposed and the standard deviation of the
run length (SDRL) distribution of the revised m-of-k rules is also studied. This thesis
complements the work of Antzoulakos and Rakitzis in 2008b, who designed the R - mlk
rules based on ARL. The Markov chain technique is employed to compute the MRLs.
Overall, the MRL results show that the revised runs rules give better performances for
detecting small and moderate mean shifts, while maintaining the same sensitivity towards
large mean shifts, compared with the standard X chart. The MRL results are in
accordance with the results obtained by Antzoulakos and Rakitzis in 2008b, where the
runs rules are designed based on ARL. All the MRLs are computed using the Mathematica
programs, where the accuracy of the computation is verified via simulation using the
Statistical Analysis System (SAS) programs. The plots of the inner limit constant, d versus
the outer limit constant, L for the various R - mlk rules and in-control MRLs are also
provided.
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RULES BASED