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VOL. 1 | 2008 A nonparametric control chart based on the Mann-Whitney statistic
Subhabrata Chakraborti, Mark A. van de Wiel

Editor(s) N. Balakrishnan, Edsel A. Peña, Mervyn J. Silvapulle

Abstract

Nonparametric or distribution-free charts can be useful in statistical process control problems when there is limited or lack of knowledge about the underlying process distribution. In this paper, a phase II Shewhart-type chart is considered for location, based on reference data from phase I analysis and the well-known Mann-Whitney statistic. Control limits are computed using Lugannani-Rice-saddlepoint, Edgeworth, and other approximations along with Monte Carlo estimation. The derivations take account of estimation and the dependence from the use of a reference sample. An illustrative numerical example is presented. The in-control performance of the proposed chart is shown to be much superior to the classical Shewhart chart. Further comparisons on the basis of some percentiles of the out-of-control conditional run length distribution and the unconditional out-of-control ARL show that the proposed chart is almost as good as the Shewhart chart for the normal distribution, but is more powerful for a heavy-tailed distribution such as the Laplace, or for a skewed distribution such as the Gamma. Interactive software, enabling a complete implementation of the chart, is made available on a website.

Information

Published: 1 January 2008
First available in Project Euclid: 1 April 2008

MathSciNet: MR2462204

Digital Object Identifier: 10.1214/193940307000000112

Subjects:
Primary: 62-07 , 62G30 , 62P30

Keywords: ARL and run length percentiles , conditioning method , distribution-free , Monte Carlo estimation , Parameter estimation , phase I and phase II , saddlepoint and edgeworth approximations , Shewhart X̄ chart , statistical process control

Rights: Copyright © 2008, Institute of Mathematical Statistics

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