Side-sensitive group runs double sampling (SSGRDS) chart for detecting mean shifts

This paper proposes a side-sensitive group runs double sampling (SSGRDS) chart to detect shifts in the process mean. It improves the side-sensitive group runs chart proposed by Gadre and Rattihalli. The implementation of the SSGRDS chart is explained. The newly developed SSGRDS chart is compared with the synthetic, double sampling, synthetic double sampling, side-sensitive group runs and exponentially weighted moving average charts, in terms of the zero-state and steady-state average number of observations to signal (ANOS) and expected average number of observations to signal (EANOS). The zero-state and steady-state ANOS (ssANOS) and EANOS results reveal that the optimal SSGRDS chart generally performs well for detecting small and large mean shifts, from an overall perspective, compared with the optimal versions of other competing charts. This article provides tables of optimal charting parameters to facilitate the design of the SSGRDS chart. From these tables, the user can directly determine the optimal charting parameters for (i) minimising the standardised mean shift δopt$ \left( {\delta _{{{\text{opt}}}} } \right) $, based on different combinations of in-control ANOS ANOS0$ \left( {ANOS_{0} } \right) $ and in-control average sample size ASS0$ \left( {ASS_{0} } \right) $, or (ii) minimising an overall range of shifts δmin,δmax$ \left( {\delta _{{\min }} ,\delta _{{\max }} } \right) $, based on different in-control EANOS EANOS0$ \left( {EANOS_{0} } \right) $ and ASS0 combinations.