Control charts for health care monitoring under intermittent
University of Twente, Department of Applied Mathematics
7500 AE Enschede, The Netherlands
1. Introduction and motivation
In health care monitoring we are typically dealing with attribute data for which the rate of failure
(malfunctioning equipment, surgical error, recurrence of cancer) p should be (very) small. For some review
material, see e.g. Sonesson and Bock(2003) and Shaha(1995). Suitable control charts in this situation can be
based on waiting times till r failures have occurred, with usually 1 r5. If such a negative binomially
distributed waiting time is too small, a signal is given. In Albers(2010) the optimal choice of r is derived and
estimation of the typically unknown p on the basis of a Phase I sample is discussed. Because of the small
false alarm rates (FAR's) involved, the estimation effects involved are not at all negligible and suitable
corrections are derived.
Quite often p will vary from patient to patient and such heterogeneity will lead to overdispersion.
Assuming a negative binomial distribution then no longer is correct and a nonparametric approach becomes
attractive. However, the small probabilities involved often ruin this possibility: Phase I samples will usually