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

Abstract

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. Copyright © 2016 John Wiley & Sons, Ltd.