A nonparametric control chart based on the Mann-Whitney statistic
| dc.creator | Chakraborti, Subhabrata | |
| dc.creator | van de Wiel, Mark A. | |
| dc.date | 2008-05-15 | |
| dc.date.accessioned | 2026-07-07T12:18:55Z | |
| dc.date.available | 2026-07-07T12:18:55Z | |
| dc.description | 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 $\bar{X}$ 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 $\bar{X}$ 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. | |
| dc.description | Published in at http://dx.doi.org/10.1214/193940307000000112 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0805.2292 | |
| dc.identifier | http://arxiv.org/abs/0805.2292 | |
| dc.identifier | IMS Collections 2008, Vol. 1, 156-172 | |
| dc.identifier | doi:10.1214/193940307000000112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212579 | |
| dc.subject | Methodology | |
| dc.subject | 62G30, 62-07, 62P30 (Primary) | |
| dc.title | A nonparametric control chart based on the Mann-Whitney statistic | |
| dc.type | text |