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2004•Quality and Reliability Engineering InternationalRequires access

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

Michael B. C. Khoo, Eng-Khoon Lim

Open publisher page 13 citations

Abstract

Abstract 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.

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What this paper is about

Abstract 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.

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Available abstract

Abstract 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.

Key concepts: Control chart, X-bar chart, Control limits, Statistics, Chart, \bar x and R chart, EWMA chart, Range (aeronautics)

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