Summary: Improved Binomial charts for monitoring
Department of Applied Mathematics
University of Twente
P.O. Box 217, 7500 AE Enschede
Abstract. For processes concerning attribute data with (very) small failure rate p, often negative binomial
control charts are used. The decision whether to stop or continue is made each time r failures have occurred,
for some r 1. Finding the optimal r for detecting a given increase of p first requires alignment of the charts
in terms of in-control behavior. In the present paper binomial charts are subjected to this same requirement.
Subsequent study reveals that the resulting charts are quite attractive in several aspects, such as detection
power. For the case of unknown p, an estimated version of the chart is derived and studied.
Keywords and phrases: Statistical Process Control, health care monitoring, geometric charts, average run length,
2000 Mathematics Subject Classification: 62P10, 62C05, 62F12
1 Introduction and motivation
Due to continuing efforts to raise production standards, the occurrence of high-quality
processes in industrial production becomes more and more common. Another area where
(very) small fractions of defectives are typical is that of health care monitoring. Failures like