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Nonparametric or distribution-free charts can be useful in statisticalprocess control problems when there is limited or lack of knowledge about theunderlying process distribution. In this paper, a phase II Shewhart-type chartis considered for location, based on reference data from phase I analysis andthe well-known Mann-Whitney statistic. Control limits are computed usingLugannani-Rice-saddlepoint, Edgeworth, and other approximations along withMonte Carlo estimation. The derivations take account of estimation and thedependence from the use of a reference sample. An illustrative numericalexample is presented. The in-control performance of the proposed chart is shownto be much superior to the classical Shewhart $\bar{X}$ chart. Furthercomparisons on the basis of some percentiles of the out-of-control conditionalrun length distribution and the unconditional out-of-control ARL show that theproposed chart is almost as good as the Shewhart $\bar{X}$ chart for the normaldistribution, but is more powerful for a heavy-tailed distribution such as theLaplace, or for a skewed distribution such as the Gamma. Interactive software,enabling a complete implementation of the chart, is made available on awebsite.

A nonparametric control chart based on the Mann-Whitney statistic