Empirical nonparametric control charts for high-quality processes

For attribute data with (very) small failure rates often control charts are used which decide whether to stop or to continue each time r failures have occurred, for some r$\geq$1. Because of the small probabilities involved, such charts are very sensitive to estimation effects. This is true in particular if the underlying failure rate varies and hence the distributions involved are not geometric. Such a situation calls for a nonparametric approach, but this may require far more Phase I observations than are typically available in practice. In the present paper it is shown how this obstacle can be effectively overcome by looking not at the sum but rather at the maximum of each group of size r.