A risk adjusted self-starting Bernoulli CUSUM control chart with dynamic probability control limits

Usually, in monitoring schemes the nominal value of the process parameter is assumed known. However, this assumption is violated owing to costly sampling and lack of data particularly in healthcare systems. On the other hand, applying a fixed control limit for the risk-adjusted Bernoulli chart causes to a variable in-control average run length performance for patient populations with dissimilar risk score distributions in monitoring clinical and surgical performance. To solve these problems, a self-starting scheme is proposed based on a parametric bootstrap method and dynamic probability control limits for the risk-adjusted Bernoulli cumulative sum control charts. The advantage of the proposed control charts lies in the use of probability control limits when any assumptions about the patients’ risk distributions and process parameter. Simulation studies show that both proposed schemes have good performance under various shifts.