Two adaptive approaches to monitoring dynamically accumulating warranty claims

Warranty claims data contain valuable information that can be extracted for early detection of reliability problems originating from product design and manufacturing. Monitoring these claims is challenging due to the heterogeneous and dynamically evolving nature of the warranted population. Existing approaches either monitor aggregate claims from the entire population, which lose critical production-sequence information for detecting underlying change points, or leverage multi-chart schemes with double stratification, which suffer from operational complexity and data scarcity. A more balanced strategy is to stratify the heterogeneous claims data solely by production batch (period). This, however, introduces a unique methodological challenge—dynamically changing observations (DCO), where observations for each production batch are not static but evolve over time. To tackle the challenge, this paper proposes two adaptive one-chart schemes based on distinct monitoring mechanisms: ReCUSUM, which offers a simple solution by adapting the CUSUM implementation to recompute statistics from scratch at each time point; and OCPM, which adopts an online change-point detection framework that provides robust performance and additionally yields diagnostic change-point estimates upon alarms. To accommodate the stochastic production-sales-claims process, we develop simulation-based dynamic control limit design algorithms to maintain the conditional false alarm rate. Comprehensive simulations and a case study demonstrate that the proposed approaches effectively resolve the DCO challenge and exhibit certain advantages over a state-of-the-art approach utilizing unstratified data, particularly for detecting late-occurring large shifts. These two approaches deliver strongly competitive solutions for monitoring dynamically accumulating warranty claims. Practical guidance on scheme selection and implementation is provided.