Fully Bayesian reliability assessment of multi-state systems with overlapping data

The failure data at the system level are often limited, resulting in high uncertainty to system reliability assessment. Integrating data drawn from various structural levels of the target system (e.g. the system, subsystems, assemblies and components), i.e. the multi-level data, through Bayesian analysis can improve the precision of system reliability assessment. However, if the multi-level data are overlapping, it is challenging for Bayesian integration to develop the likelihood function. Especially for multi-state systems (MSS), the Bayesian integration with overlapping data is even more difficult. The major disadvantage of previous approaches is the intensive computation for the development of the likelihood function caused by the workload to opt the appropriate combinations of the vectors of component states consistent with the overlapping data. An improved fully Bayesian integration approach from a geometric perspective is proposed for the reliability assessment of MSS with overlapping data. In this method, a specific combination of component states is regarded as a state vector, which leads to a specific system state of the MSS, and all state vectors generate a system state space. The overlapping data are regarded as the constraints which create hyperplanes in the system state space. And a point in a hyperplane corresponds to a particular combination of the state vectors. In the light of the features of the constraints, the proposed approach introduces space partition and hyperplane segmentation, which reduces the selection workload significantly and simplifies the likelihood function for overlapping data. Two examples demonstrate the feasibility and efficiency of the proposed approach.