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Reliability assessment is a crucial activity for engineered systems as the results are able to provide valuable information for reliability-related decisions, such as maintenance planning and warranty policy. Nevertheless, accurately assessing the system reliability is challenging if only some pieces of reliability-related data can be collected from experts. Such data may be, however, imprecise, heterogeneous, and from multiple physical levels of a system. In this paper, a constrained optimization model is put forth to assess the system reliability by fusing multi-source of imprecise reliability data. Firstly, a set of constraints is constructed for a resulting optimization model by representing various imprecise reliability data as functions of unknown parameters associated with degradation models of components. Secondly, by maximizing and minimizing system reliability function, the upper and lower bounds of system reliability can be evaluated. Finally, a model selection approach is developed to identify component degradation model which matches up with all the imprecise reliability data to the maximum extent. An illustrative example shows that system reliability over time can be effectively evaluated by fusing imprecise reliability data. The conflicts among multi-source of imprecise reliability data can be properly avoided by identifying the feasible region of all the unknown parameters in which all the constraints can be satisfied.

By utilizing inspection data, reliability of a particular individual system can be dynamically updated. In view of the hierarchical structure of engineering systems, inspection data can be collected from multiple physical levels of a system. Nevertheless, due to the limited inspection resources, such as time, budget, and manpower, simultaneously inspecting all the components, subsystems, and the entire system is unaffordable. It, therefore, raises a natural question: how to identify the optimal inspection strategy under limited resources to reveal the health states of a system and its components to the maximum extent. To address the above question, a new metric is proposed in this paper to quantify the effectiveness of a particular inspection strategy in terms of revealing the states of components in a multi-state system. The optimal multi-level inspection strategy for the system is, thereby, determined by maximizing the proposed metric under limited inspection resources. An illustrative example shows that the proposed method can optimally allocate the limited inspection resources, so as to maximally reveal the states of components of interest and facilitate dynamic reliability assessment of a system.