  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.
