The Use of R and S2 Charts Under Nonstandard Conditions.
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG
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R and S-squared charts for monitoring the variability of a process are studied when the control variance, sigma sub 0 squared is unknown, when observations are non-Gaussian, and when the process drifts. Geometric bounds on run-length distributions for the R and S-squared charts are given for all underlying distributions when sigma sub 0 squared is estimated in a base period. Similar bounds apply in the case of a drifting process, the notion of which is developed rigorously. It is shown that normal-theory properties of these charts hold exactly for every spherical process when a suitable estimate for sigma sub 0 squared is used. Run-length distributions otherwise are shown to be ordered stochastically given a peakedness ordering on the underlying spherical processes. Author
- Statistics and Probability