Page 202 - Special Topic Session (STS) - Volume 3

STS540 Zhi Lin C. et al.
In recent years, Wu and Spedding (2000) introduced the synthetic scheme
through the combination of the Shewhart sub-chart with the Conforming
̅
Run Length () sub-chart. They showed that the synthetic scheme surpasses
the traditional Shewhart scheme under all magnitudes of mean shifts and
̅
also outperforms the EWMA scheme for mean shift sizes > 0.8. As an effort
̅
to improve the synthetic scheme, Gadre and Rattihalli (2004) introduced the
Group Runs (GR) scheme by incorporating the Shewhart sub-chart with an
̅
improved version of the sub-chart. Moreover, Gadre and Rattihalli (2006)
further improved the GR scheme by introducing the Modified GR (MGR)
scheme. Then, Gadre and Rattihalli (2007) introduced the Side-Sensitive GR
(SSGR) scheme, which is essentially a GR scheme with the side-sensitive
feature. The Side-Sensitive MGR (SSMGR) scheme was proposed by (2010),
which is essentially a MGR scheme with the side-sensitive feature.
Recently, the GR-type schemes are widely investigated by numerous
researchers. You et al. (2015) studied the SSGR scheme in the scenario where
the process parameters are unknown and have to be estimated from a Phase-
I sample. Lim et al. (2015) scrutinized the economic and economic statistical
designs of the SSGR scheme by minimizing the cost. Chong et al. (2017)
introduced the GR revised m-of-k runs rules scheme by combining the GR
scheme and revised m-of-k runs rules scheme proposed by Antzoulakos and
Rakitzis (2008). Chong et al. (2019) investigated the MGR scheme when the
process parameters are unknown.
This study is motivated by Yew et al. (2016) who considered the
performance comparison of the GR and SSGR schemes using the average time
to signal () criterion. However, as in all the GR-type schemes mentioned
above, Yew et al. (2016) did not consider the performance of the standard
deviation of the time to signal () between the GR and SSGR schemes. In
the performance comparison using the criterion, the scheme with the
lowest is desirable as it demonstrates that the variability of time to signal
distribution of the scheme is lower and hence its performance is more
predictable. Therefore, the aim of this study is to examine the
performance of the GR and SSGR schemes.

2. Operations of the GR and SSGR schemes:
The operations of the GR and SSGR schemes are given in this section.
2.1 The GR Scheme:
The GR scheme is proposed as an extension of the synthetic scheme. Similar
to the synthetic scheme, for the GR scheme, a point plotted outside the control
limits of the sub-chart is not immediately treated as an OC signal, but just a
̅
nonconforming sample, awaiting the decision from the CRL sub-chart. We define
the CRL value as the number of conforming samples between the previous
(excluded in the count) and current (included in the count) nonconforming

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