Reliability Analysis and Component Importance Assessment for k-out-of-n Systems with Uncertain Continuous States and Uncertain Weights

Engineering systems generally exhibit continuous state degradation in practical operation, and reliability evaluation is often challenged by data scarcity and uncertain component weights. Existing studies on weighted k-out-of-n systems mainly focus on deterministic or discrete-state models, while rarely addressing reliability modeling and component importance assessment for continuous-state systems with uncertain information under data shortage, which constitutes a clear research gap. This paper first defines the connotation of uncertain continuous state as the continuous degradation process of system performance affected by ambiguous parameter information and insufficient historical data. On this basis, a reliability modeling framework is established for a weighted k-out-of-n system with uncertain continuous states. Adopting stochastic reliability theory, this paper comparatively investigates system reliability under constant component weights and uncertain variable component weights, and further adopts the Birnbaum importance measure to quantify component importance under variable weight uncertainty. To reduce computational complexity and improve solution efficiency, a binary search-based numerical algorithm is developed to solve the established model. A distributed solar power generation system is employed as a practical case to validate the feasibility and applicability of the proposed model and algorithm. The presented approach effectively fills the limitation of existing discrete and deterministic models, and provides a novel theoretical reference for reliability analysis and key component identification of continuous degradation engineering systems.