A synthetic double sampling control chart for the process mean

This article proposes a synthetic double sampling chart that integrates the Double Sampling (DS) X̄ chart and the conforming run length chart. The proposed procedure offers performance improvements in terms of the zero-state Average Run Length (ARL) and Average Number of Observations to Sample (ANOS). When the size of a mean shift (given in terms of the number of standard deviation units) is small (i.e., between 0.4 and 0.6) and the mean sample size n= 5, the proposed procedure reduces the out-of-control ARL and ANOS values by nearly half, compared with both the synthetic and DS X̄ charts. In terms of detection ability versus the Exponentially Weighted Moving Average (EWMA) chart, the synthetic DS chart is superior to the synthetic or even the DS X̄ chart, as the former outperforms the EWMA chart for a larger range of values compared to the latter. The proposed procedure generally outperforms the EWMA chart in the detection of a mean shift when is larger than 0.5 and n= 5 or 10. Although the proposed procedure is less sensitive than the EWMA chart when is smaller than 0.5, this may not be a setback as it is usually not desirable, from a practical viewpoint, to signal very small shifts in the process to avoid too frequent process interruptions. Instead, under such circumstances, it is better to leave the process undisturbed.