This paper proposes a two-stage weighted k-out-of-n (W-k/n) system reliability model based on uncertainty theory to address the problem of traditional W-k/n system theory being difficult to apply to the reliability evaluation of complex systems with two-layer structures. This model effectively solves the evaluation problem in the case of insufficient data by decomposing the reliability assessment of complex systems into two stages: system structure reliability and subsystem reliability. In the model, the system state and weights are described by uncertain variables that follow a certain distribution. Under the framework of uncertainty theory, two-stage reliability measures and importance measures are defined, and corresponding calculation formulas are derived. In order to reduce computational complexity, a corresponding numerical solution method including traverse search algorithm and binary search algorithm is proposed. The effectiveness of the method is also demonstrated through a project management case of electronic consumer goods. This study provides new theoretical ideas and methodological support for reliability modeling of complex systems under data loss conditions.

A class of complex systems can be structurally decomposed into several typical multi-state weighted k/n systems. In view of this, this paper proposes a reliability model to evaluate the reliability of such systems. The system reliability evaluation process is divided into two critical stages: (1) Primary stage: Structural reliability analysis (system-level) and (2) Secondary stage: Subsystem reliability verification (component-level). In practical applications, when there is a lack of operational data, expert experience is needed to evaluate the states and availability weights of components, which is a typical application scenario for uncertainty theory. Under the framework of uncertainty theory, two-stage reliability measures and importance measures are defined, and corresponding calculation formulas are derived. To improve computational efficiency, a binary search algorithm is proposed. Finally, an application case of SDN was proposed to demonstrate the effectiveness of the theory and method. This study provides an idea for the reliability modeling of complex systems (multiple pipeline transmissions, power systems, distributed computing, etc.) in the absence of operational data.

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.