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Dynamic probability control limits for risk‐adjusted Bernoulli CUSUM charts
Author(s) -
Zhang Xiang,
Woodall William H.
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6547
Subject(s) - cusum , control chart , bernoulli's principle , computer science , control limits , statistics , chart , shewhart individuals control chart , false alarm , limit (mathematics) , conditional probability , statistical process control , mathematics , ewma chart , engineering , mathematical analysis , process (computing) , aerospace engineering , operating system
The risk‐adjusted Bernoulli cumulative sum (CUSUM) chart developed by Steiner et al. (2000) is an increasingly popular tool for monitoring clinical and surgical performance. In practice, however, the use of a fixed control limit for the chart leads to a quite variable in‐control average run length performance for patient populations with different risk score distributions. To overcome this problem, we determine simulation‐based dynamic probability control limits (DPCLs) patient‐by‐patient for the risk‐adjusted Bernoulli CUSUM charts. By maintaining the probability of a false alarm at a constant level conditional on no false alarm for previous observations, our risk‐adjusted CUSUM charts with DPCLs have consistent in‐control performance at the desired level with approximately geometrically distributed run lengths. Our simulation results demonstrate that our method does not rely on any information or assumptions about the patients' risk distributions. The use of DPCLs for risk‐adjusted Bernoulli CUSUM charts allows each chart to be designed for the corresponding particular sequence of patients for a surgeon or hospital. Copyright © 2015 John Wiley & Sons, Ltd.