The Effect of Estimation Error on Risk-adjusted Bernoulli GEWMA Control Chart in Multistage Healthcare Processes

Background and objectives: Risk-adjusted Bernoulli control chart is one of the main tools for monitoring multistage healthcare processes to achieve higher performance and effectiveness in healthcare settings. Using parameter estimates can lead to significantly deteriorate chart performance. However, so far, the effect of estimation error on this chart in which healthcare services delivery is considered as Bernoulli response variable has not been surveyed. Methods: We examined the effect of estimation error on the in- and out-control performance of Bernoulli Group Exponentially Weighted Moving Average (GEWMA) risk-adjusted chart for multistage healthcare processes. In this paper, the effect of estimation error is indicated by run length properties using repeated sampling of the data under different scenarios in both in- and out-of-control situations. In this regard, three methods of increasing sample size, adjusting control limit, and applying Dynamic Probability Control Limits (DPCL) are proposed to diminish the effect of estimation error on the proposed chart. Also, DPCL are applied in both zero- and steady-states. Results: Simulation results showed that estimation error can have a substantial effect on Bernoulli GEWMA risk-adjusted chart performance. Also, results show that the effect of estimation error can be serious, especially if small samples are applied. Using our simulation, control limit can be adjusted in a given sample size to reduce the effect of parameter estimation for medical situations in which there is not enough sampling data. Conclusion: Applying the DPCL has the superior performance than the other proposed methods to reduce the estimation error especially in steady state. Moreover, a comprehensive analysis on results allows us to provide suitable sample size recommendations in constructing these charts to reach a desired hospital performance.