 
Summary: Empirical nonparametric control charts for
highquality processes
Willem Albers
Department of Applied Mathematics
University of Twente
P.O. Box 217, 7500 AE Enschede
The Netherlands
Abstract. 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 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.
Keywords and phrases: Statistical Process Control, health care monitoring, geometric charts, average run length,
estimated parameters, order statistics
2000 Mathematics Subject Classification: 62P10, 62C05, 62G15
1 Introduction and motivation
Highquality processes are by now a regular phenomenon in industrial settings, due tot
the fact that production standards have been increasing over the last few decades. Moreover,
