Real-time monitoring of insurance claims predictions using hybrid neuro-fuzzy control charts with applications to health insurance

In non-life insurance, reserve predictions are often determined at a fixed valuation date using the chain-ladder (CL) method and subsequently updated by applying the initially estimated development factors to newly observed claim amounts. Although this approach is widely used for reserve back-testing, it provides limited support for the continuous monitoring of the adequacy and stability of reserve predictions over time, particularly in the presence of structural changes or concept drift. This paper proposes a real-time monitoring framework for CL-based reserve predictions that integrates statistical control charts—one of the foundational tools in statistical process control (SPC)—with an adaptive neuro-fuzzy inference system (ANFIS). Instead of forecasting future claims, the framework continuously compares observed claims developments against CL-based predictions. Simulation studies covering ( i ) complete claims development data, ( ii ) varying noise levels, ( iii ) shift detection in updated claims, and ( iv ) detecting shifts in nonparametric state changes in the claims demonstrate that the proposed hybrid ANFIS-SPC model leads to an improved detection performance. To quantify the detection ability, the average run length (ARL) is employed for measuring the speed of change detection in the process. Across all considered scenarios, the proposed control chart demonstrates consistently better out-of-control (OOC) ARL values than the benchmark methods. The improvement varies across shift magnitudes, ranging from modest for small process changes to substantial for larger shifts, highlighting the method’s strong and adaptable detection performance. An illustrative example based on short-tail dental insurance data further validates the framework’s practical utility and effectiveness for online monitoring of insurance reserve predictions.