On the Effect of Estimation Error for the Risk-Adjusted Charts

Control charts are a popular statistical process control (SPC) technique for monitoring to detect the unusual variations in different processes. Contrary to the classical charts, control charts have also been modified to include covariates using regression approaches. This study assesses the performance of risk-adjusted control charts under the complexity of estimation error by considering logistic and negative binomial regression models. To be more precise, risk-adjusted Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts are used to evaluate the impact of the estimation error. To compute the average run length (ARL), Markov Chain Monte Carlo simulations are conducted. Furthermore, a bootstrap method is also used to compute the ARL assuming different Phase-I data sets to minimize the effect of estimation error on risk-adjusted control charts. The results for cardiac surgery and respiratory disease data sets show that the modified control charts improve the performance in detecting small shifts.