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Quality control using S 2 or S charts for subgroups of varying sample sizes and their exact average run lengths
Author(s) -
Maghsoodloo Saeed,
Shirzaei Samira
Publication year - 2021
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2847
Subject(s) - statistics , control chart , mathematics , estimator , sample size determination , chart , section (typography) , sample (material) , x bar chart , control limits , standard deviation , \bar x and r chart , statistical process control , computer science , process (computing) , chemistry , chromatography , operating system
This article generalizes the historical S 2 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 M> 1 subgroups of equal sample sizes from a normal universe. Section 3 provides the general probability control limits (CONLs) for the S 2 chart of unequal sample sizes. Section 4 uses the chi‐square distribution to obtain the exact α ‐level CONLs for the S chart. Section 5 proves that the average run length (ARL) of S and S 2 charts are identical and tabulates the ARL for the most common sample sizes n = 2, 3, … , and 12. Further, as expected, the ARL of S charts always perform better than those of the corresponding R charts.