Reliability Assessment of a Hierarchical System Subjected to Inconsistent Priors and Multilevel Data

The reliability assessment for a system with multiple prior information can be challenging. In this paper, we propose a novel Bayesian melding (BM) approach to combine the inconsistent prior distributions. This approach is first investigated to address a flaw in traditional BM methods and then extended to a general multilevel hierarchical system with biased priors and limited data. We realize our method via an improved importance sampling technique, which is intuitive and especially convenient for routine program. A simple numerical case is presented to illustrate the problem at stake and the idea behind our approach, followed with a practical case to demonstrate its usefulness in reliability engineering. The results show our approach has some superiorities in parameter estimation and reliability assessment compared with existing studies under nonideal circumstances, i.e., with biased priors and limited data. This approach provides insights into reliability assessment of a system/product in its early usage period, where the test data is usually limited and the prior information is always inaccurate.