## Institute of Mathematical Statistics Collections

- Collections
- Volume 1, 2008, 156-172

### A nonparametric control chart based on the Mann-Whitney statistic

Subhabrata Chakraborti and Mark A. van de Wiel

#### 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 *X̄* 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 *X̄* 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.

#### Chapter information

**Source***Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen* (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008)

**Dates**

First available in Project Euclid: 1 April 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.imsc/1207058271

**Digital Object Identifier**

doi:10.1214/193940307000000112

**Mathematical Reviews number (MathSciNet)**

MR2462204

**Subjects**

Primary: 62G30: Order statistics; empirical distribution functions 62-07: Data analysis 62P30: Applications in engineering and industry

**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

#### Citation

Chakraborti, Subhabrata; van de Wiel, Mark A. A nonparametric control chart based on the Mann-Whitney statistic. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 156--172, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000112. https://projecteuclid.org/euclid.imsc/1207058271

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