Reliability bounds for multi-state systems by fusing multiple sources of imprecise information

It is crucial to evaluate reliability measures of a system over time, so that reliability-related decisions, such as maintenance planning and warranty policy, can be appropriately made for the system. However, accurately assessing system reliability becomes challenging if only limited amounts of reliability data are available. On the other hand, imprecise information related to reliability measures of a system can be collected based on experts' judgments/experiences, and these pieces of information may be, however, heterogeneous and come from multiple sources. By properly fusing the imprecise information, reliability bounds of a system can be assessed to facilitate the ensuing reliability-related decision-making. In this article, a constrained optimization framework is proposed to assess reliability bounds of multi-state systems by fusing multiple sources of imprecise information. The proposed framework is composed of three basic steps: (i) constructing a set of constraints for a resulting optimization formulation by representing all the imprecise information as functions of unknown parameters of the degradation models for components; (ii) identifying the upper and lower bounds of the system reliability function by resolving the resulting constrained optimization problem via a tailored feasibility-based particle swarm algorithm; and (iii) developing a model selection approach to choose the best component degradation model that matches with all the imprecise information to the maximum extent. A numerical example along with an engineering example is given to demonstrate the effectiveness of the proposed method.