Reliability of two-stage competing failure systems with dynamic load adjustment

• Published in: Applied mathematical modelling Vol. 149; p. 116303
• Main Authors: Dong, Qinglai, Zhang, Yuepeng, Wang, Ning
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2026
• Subjects: Competing risks; Load level adjustment; Reliability assessment; Two-stage degradation; UAV systems; Load level adjustment; Reliability assessment; Two-stage degradation; Competing risks; UAV systems
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2025.116303

Many engineering systems are prone to failure due to the combined influence of internal degradation and external random shocks. In such systems, degradation progression exhibits explicit load dependence. Current reliability models often overlook the critical interactions between environmental variability and load-dependent failure mechanisms. This paper develops an integrated framework by combining a two-phase load adjustment policy that dynamically regulates production rates to control degradation rates and a delay time reliability model to incorporate environmental uncertainty. Theoretical analysis and numerical simulations demonstrate that the proposed strategy effectively optimizes periodic inspection intervals under varying load conditions and enables system adjustment to a low-load operational mode upon defect detection. This approach significantly reduces the long-term average maintenance cost arising from competing failure mechanisms. Implementation in an unmanned aerial vehicle (UAV) system demonstrates the model's practical effectiveness, achieving substantial operational cost savings compared to fixed-load strategies. The proposed methodology provides a decision-support tool for industrial systems requiring balanced production efficiency and reliability. •Novel load-dependent two-stage failure model with external shocks.•State-triggered load level adjustment strategy reduces failure risks.•Hybrid policy optimizes load adjustment and cost trade-offs.