 
Summary: Risk adjusted control charts for health care
monitoring
Willem Albers
Department of Applied Mathematics
University of Twente
P.O. Box 217, 7500 AE Enschede
The Netherlands
Abstract. Attribute data from high quality processes can be monitored effectively by deciding on whether or
not to stop at each time where r 1 failures have occurred. The smaller the degree of change in failure rate
during OutofControl one wants to be optimally protected against, the larger r should be. Under homogeneity,
the distribution involved is negative binomial. However, in health care monitoring, (groups of) patients will
often belong to different risk categories. In the present paper we will show how information about category
membership can be used to adjust the basic negative binomial charts to the actual risk incurred. Attention
is also devoted to comparing such conditional charts to their unconditional counterparts. The latter do take
possible heterogeneity into account, but refrain from risk adjustment. Note that in the risk adjusted case several
parameters are involved, which will typically all be unknown. Hence the potentially considerable estimation
effects of the new charts will be investigated as well.
Keywords and phrases: Statistical Process Control, highquality processes, geometric charts, average run length,
estimated parameters, heterogeneity
2000 Mathematics Subject Classification: 62P10, 62C05, 62F12
