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Reliability assessment of multi-state systems (MSSs), which can characterize complex degradation processes of components by introducing several intermediate states, has received tremendous attention in recent years. In the domain of the reliability assessment of MSSs, expert opinions are oftentimes utilized to compensate for the poor quantity of failure/degradation data. Therefore, many approaches aiming to fuse multiple expert opinions which may be imprecise, have been developed to carry out a comprehensive reliability estimate for MSSs. In this procedure, however, reliabilities estimated from different experts are oftentimes conflicting with each other owing to various knowledge backgrounds of experts, which causes difficulty in the subsequent fusion of reliability results. Therefore, how to primarily measure the conflicts and calibrate such conflicting opinions to reach a consensus on reliability estimate remains unresolved matters. In this article, we propose a reliability
consensus reaching model with the objective of minimizing the total calibration values of expert opinions under a consensus threshold. In the first place, to realize the reliability assessment of MSSs, we utilized the evidential networks to infer the system reliability bounds
by using each expert imprecise information. On this basis, individual opinions from all experts are aggregated to a collective opinion which reflects the group consensus by an ordered weighted averaging (OWA) operator. To satisfy the requirement of an optimistic or pessimistic attitude towards the reliability assessment results, the weight of aggregation is to be adjusted for the customized calibration results with preference. Subsequently, Jousselme distances between individual opinions and the collective opinion are defined for the
quantization of conflicts between expert opinions, and correspondingly, the degree of consensus is proposed. According to the consensus index, expert opinions will be calibrated to meet the consensus threshold. In this procedure, conflicting opinions will gradually reach consistency. A particle swarm optimization algorithm with constraints is implemented for realization of the consensus reaching procedure. By designing a numerical example as well as
an engineering application, the effectiveness of the proposed method is demonstrated. On the one hand, along with the increase of consensus thresholds, the reliability bounds containing conflicts initially tends to be consistent and the total value of calibration tends to be larger, which coincides with intuition. In addition, the larger threshold of consensus makes the adjustment results stable, which indicates that the fewer candidate combinations of calibration
to reach. On the other hand, the selection of the aggregation weight for individual opinions of reliability also has impacts on the results of total calibration values. Specifically, when we have no preference to reliability estimate, the value reaches minimum. Once we have optimistic or pessimistic preference on the reliability estimate, the calibration value becomes larger.

Multi-state systems (MSSs), Evidential network, Calibration of expert opinions, Consensus reaching