A synthetic double sampling control chart for the process mean

This article proposes a synthetic double sampling chart that integrates the Double Sampling (DS) [image omitted] 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 [image omitted] 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 [image omitted] 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.