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STS540 Zhi Lin C. et al.
4.2 Performance comparison between the GR and SSGR schemes (OC )
In this subsection, we compare the performance of the OC (1)
between the GR and SSGR schemes, i.e. case >0 in Tables 2 to 4. From Tables
2 to 4, we notice that when < 2.0, the SSGR scheme has consistently lower
1 compared to the GR scheme except for two cases, i.e. (, opt, 0) =
(7, 1.0, 370) and (7, 1.0, 500) when = 1.0; whereas when > 2.0, the SSGR
scheme has either slightly lower or almost the same 1 compared to the
GR scheme. Therefore, we conclude that the SSGR scheme has a superior
1 performance compared to GR scheme. The 1 result,
complemented with the 1 result in Yew et al. (2016), showed that the SSGR
scheme prevails over the GR scheme in terms of 1 and 1.

5. Conclusions
In this paper, we perform an in-depth SDTS performance comparison
between the GR and SSGR schemes. We utilize the ScicosLab software to
compute the optimal parameters of the GR and SSGR schemes by minimizing
the ATS1. Then, we use the SAS software to calculate the SDTS of the GR and
SSGR schemes for various mean shift sizes . From the performance
comparison, we
conclude that the GR scheme slightly surpasses the SSGR scheme in terms of
SDTS0 performance. However, the opposite is true for the SDTS1, where the
SSGR scheme outperforms the GR scheme. This indicates that although
practitioners are encouraged to use the SSGR scheme due to its superior
SDTS1 performance, they should not ignore the fact that the performance of
the SSGR scheme is slightly inferior to the GR scheme in terms of SDTS0 and it
may lead to a higher early false alarm than the GR scheme. Future research
can compare the performance of the GR and SSGR schemes in terms of SDTS
by minimizing the OC median time to signal (MTS1) instead of the ATS1, since
the median is less affected by outliers compared to the average.

References
1. Antzoulakos, D.L. & Rakitzis, A.C. (2008). The revised m-of-k runs rule.
Qual. Eng., 20, 75–81. Chong, Z.L., Khoo, M.B.C., Lee, M.H. & Chen, C.H.
(2017). Group runs revised m-of-k runs rule control chart. Commun. Stat.
Theory Methods, 46, 6916–6935.
2. Chong, Z.L., Khoo, M.B.C., Teoh, W.L., Yeong, W.C. & Lim, S.L. (2019).
Optimal design of the modified group runs (MGR) X chart when process
parameters are estimated. Commun. Stat. Simul. Comput., to be
published.
3. Gadre, M.P. & Rattihalli, R.N. (2004). A group runs control chart for
detecting shifts in the process mean. Econ. Qual. Contr., 19, 29−43.

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