A modified variable sample size and sampling interval controlchart

In this article, a modified version of variable sample size and sampling interval chart using three sampling intervals and two sample sizes, called the VSSIt control chart, is proposed to overcome the weakness of the standard Shewhart (SS) control chart in detecting small and moderate shifts. In order to evaluate the performance of the proposed scheme, average time to signal (ATS), average number of observations to signal (ANOS), and average number of samples to signal (ANSS) are used. Using this control chart can reduce the ATS value around 68, 27, 7, and 1.83 time unit (sampling interval of the SS chart) in detecting shift of size 0.25, 0.5, 0.75, and 1 standard deviation, respectively. The performance of the constructed adaptive chart is compared with various adaptive charts such as variable sample size (VSS), variable sampling interval (VSI), variable sample size and sampling interval (VSSI), and special variable sample size and sampling interval (SVSSI) x¯$$ \overline{x} $$ control chart. It is shown that the proposed chart always outperforms SS, VSI, VSS, and VSSI schemes. It also can detect shift of size 0.25 standard deviation quicker than SVSSI scheme. Finally, the optimal parameters of the proposed chart are recommended.