Design of random renewing warranties with cost-sharing for mission-oriented products

The rapid evolution of digital technologies is fundamentally transforming reliability management frameworks, necessitating the integration of innovative methodologies as central elements of reliability management modernization. This study proposes a novel random warranty model—the two-limit random renewing back warranty with cost-sharing (2LRRBW CS), from a manufacturer perspective, designed to enhance warranty coverage reliability for mission-critical products. The framework includes several variant models to address different operational scenarios. Comprehensive numerical analyses are performed to elucidate the fundamental variation patterns and operational mechanisms inherent in the proposed warranty models.