A Nonparametric Control Chart based on the Mann-Whitney Statistic

Nonparametric or distribution-free charts can be useful in statistical process control when there is limited knowledge about the underlying process. In this paper a Shewhart-type chart is considered for the location, based on the Mann-Whitney statistic. The control limit calculations use Lugannani-Rice saddlepoint, Edgeworth and other approximation methods along with Monte Carlo estimation and take account of the dependence resulting from the use of a reference sample from the in-control process. Interactive software, made available on a website, enables a complete implementation of the procedure by remote users. An illustrative numerical example is presented. Performance comparisons, in terms of the in-control unconditional ARL and the 5 percentile of the conditional run length distribution show that the nonparametric chart has superior in-control properties with regard to the classical Shewhart X chart. Further comparisons of the out-of-control unconditional ARL and the 95 percentiles of the conditional run length distributions show that the proposed chart is almost as good as the X chart for the normal distribution, but is far more powerful for a heavy-tailed distribution such as the Laplace, or for a skewed distribution such as the Gamma.