Quality control using S2 or S charts for subgroups of varying sample sizes and their exact average run lengths

Abstract

AbstractThis article generalizes the historical chart (of equal sample sizes) to subgroups of differing sample sizes. As a sequel to a previous article, Section 2 compares all estimators of process standard deviation for more than 1 subgroups of equal sample sizes from a normal universe. Section 3 provides the general probability control limits (CONLs) for the chart of unequal sample sizes. Section 4 uses the chi‐square distribution to obtain the exact ‐level CONLs for the S chart. Section 5 proves that the average run length (ARL) of and charts are identical and tabulates the ARL for the most common sample sizes = 2, 3, , and 12. Further, as expected, the ARL of charts always perform better than those of the corresponding charts.