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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 895273, 16 pages
Research Article

Risk-Adjusted Control Charts for Health Care Monitoring

Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

Received 29 July 2011; Revised 2 September 2011; Accepted 6 September 2011

Academic Editor: Frank Werner

Copyright © 2011 Willem Albers. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 out of control one wants to be optimally protected against, the larger the 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 all be typically unknown. Hence, the potentially considerable estimation effects of the new charts will be investigated as well.