The comparative efficiency of the X and R Charts and L-S chart for statistical quality control
Abstract
This paper deals with the comparative efficiencies of the X and R charts and the L-S chart (L being the largest and S the smallest value of the sample) from the theoretical and practical points of view. It has been found that in practice the corrective steps suggested by both tallied almost exactly. From theoretical points, when standard deviation varies, the L-S chart is almost as efficient as the X and R charts, but with the variation in the mean the relative efficiency of the L-S chart comes down appreciably as the X and R charts, but with the variation in the mean shifts more and more from the original valueReferences
Howell, J.M. (1949): “Control chart for largest and smallest values” Ann. Math. Stat., 20, 305.
Krishna Iyer, P.V. and Bhattacharya, M.N. (1953) “lecture notes on statistical quality control and sampling inspection” (restricted).
Pearson, E.S. (1945): “ the probability integral of the range in samples of n observations from a normal population” Biometrika, 32, 301.
Sealy, E.H. (1945) : “First guide to quality control for engineers” His majority’s Stationary office,
London.
Stevens, W.L. (1948): “Control by gauging” J. Roy. Stat. Soc., B, 10, 54.
Tippet, L.H.C. (1925): “On the extreme individuals and the range of sample taken from a normal population.” Biometrika, 17, 365.
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