Reduction of the Effect of Estimation Error on In-control Performance for Risk-adjusted Bernoulli CUSUM Chart with Dynamic Probability Control Limits

The in‐control performance of any control chart is highly associated with the accuracy of estimation for the in‐control parameter(s). For the risk‐adjusted Bernoulli cumulative sum (CUSUM) chart with a constant control limit, it had been shown that the estimation error could have a substantial effect on the in‐control performance. In our study, we examine the effect of estimation error on the in‐control performance of the risk‐adjusted Bernoulli CUSUM chart with dynamic probability control limits (DPCLs). Our simulation results show that the in‐control performance of risk‐adjusted Bernoulli CUSUM chart with DPCLs is also affected by the estimation error. The most important factors affecting estimation error are the specified desired in‐control average run length, the Phase I sample size, and the adverse event rate. However, the effect of estimation error is uniformly smaller for the risk‐adjusted Bernoulli CUSUM chart with DPCLs than for the corresponding chart with a constant control limit under various realistic scenarios. In addition, we found a substantial reduction in the mean and variation of the standard deviation of the in‐control run length when DPCLs are used. Therefore, use of DPCLs has yet another advantage when designing a risk‐adjusted Bernoulli CUSUM chart.