Kurtosis correction method for &Xmacr; and R control charts for long-tailed symmetrical distributions

Kurtosis correction method for &Xmacr; and R control charts for long-tailed symmetrical distributions

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Article ID: iaor20082050
Country: United States
Volume: 54
Issue: 4
Start Page Number: 371
End Page Number: 383
Publication Date: Jun 2007
Journal: Naval Research Logistics
Authors: ,
Keywords: control processes
Abstract:

This paper proposes a kurtosis correction (KC) method for constructing the &Xmacr; and R control charts for symmetrical long-tailed (leptokurtic) distributions. The control charts are similar to the Shewhart control charts and are very easy to use. The control limits are derived based on the degree of kurtosis estimated from the actual (subgroup) data. It is assumed that the underlying quality characteristic is symmetrically distributed and no other distributional and/or parameter assumptions are made. The control chart constants are tabulated and the performance of these charts is compared with that of the Shewhart control charts. For the case of the logistic distribution, the exact control limits are derived and are compared with the KC method and the Shewhart method.

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