The double sampling range chart

TLDR: The R chart and the S2 chart are the usual charts for monitoring process dispersion; however, the double sampling (DS) scheme has only be used with the S1 chart, and the difficulty in obtaining the properties of the DS R chart might explain the lack of papers dealing with this type of DS chart.

Abstract: The R chart and the S2 chart are the usual charts for monitoring process dispersion; however, the double sampling (DS) scheme has only be used with the S2 chart. The difficulty in obtaining the properties of the DS R chart might explain the lack of papers dealing with this type of DS chart. The S2 chart has the advantage of being more efficient than the R chart, but the same is not always observed with their DS versions. Depending on the size of the 2 samples, the DS R chart performs better. The trade-off between operational simplicity and power of detection might lead the practitioner to choose the DS R chart, even with the DS S2 chart signaling faster.