Dynamic Probability Control Limits for Lower and Two-Sided Risk-Adjusted Bernoulli CUSUM Charts

Because of its advantages of design, performance, and effectiveness in reducing the effect of patients' prior risks, the risk‐adjusted Bernoulli cumulative sum (CUSUM) chart is widely applied to monitor clinical and surgical outcome performance. In practice, it is beneficial to obtain evidence of improved surgical performance using the lower risk‐adjusted Bernoulli CUSUM charts. However, it had been shown that the in‐control performance of the charts with constant control limits varies considerably for different patient populations. In our study, we apply the dynamic probability control limits (DPCLs) developed for the upper risk‐adjusted Bernoulli CUSUM charts to the lower and two‐sided charts and examine their in‐control performance. The simulation results demonstrate that the in‐control performance of the lower risk‐adjusted Bernoulli CUSUM charts with DPCLs can be controlled for different patient populations, because these limits are determined for each specific sequence of patients. In addition, practitioners could also run upper and lower risk‐adjusted Bernoulli CUSUM charts with DPCLs side by side simultaneously and obtain desired in‐control performance for the two‐sided chart for any particular sequence of patients for a surgeon or hospital.