An Improved R (Range) Control Chart for Monitoring the Process Variance

An R chart is often used to monitor shifts in the process variability. However, the range, $R_i, i = 1, 2, \dots$, statistics from a sampling distribution are highly skewed. Hence, the classical R chart based on the $\pm3\sigma$ control limits will not give an in‐control average run length of approx...

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Bibliographic Details
Published in:Quality and reliability engineering international 2005-02, Vol.21 (1), p.43-50
Main Authors: Khoo, Michael B. C., Lim, E. G.
Format: Article
Language:English
Subjects:
average run length (ARL)
in-control
out-of-control
R chart
range statistic
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Summary:An R chart is often used to monitor shifts in the process variability. However, the range, $R_i, i = 1, 2, \dots$, statistics from a sampling distribution are highly skewed. Hence, the classical R chart based on the $\pm3\sigma$ control limits will not give an in‐control average run length of approximately 370, or equivalently a type I error, $\alpha = 0.0027$. In this paper, an approach is shown to obtain the control limits of an improved R chart based on a desired type I error from the density function of the Ri statistics. Copyright © 2004 John Wiley & Sons, Ltd.
ISSN:0748-8017
1099-1638
DOI:10.1002/qre.606