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.

中文翻译：

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先验和多级数据不一致的分层系统的可靠性评估

具有多个先验信息的系统的可靠性评估可能具有挑战性。在本文中，我们提出了一种新的贝叶斯融合 (BM) 方法来组合不一致的先验分布。这种方法首先被研究以解决传统 BM 方法的缺陷，然后扩展到具有偏见先验和有限数据的一般多级层次系统。我们通过改进的重要性采样技术来实现我们的方法，这对于常规程序来说是直观且特别方便的。给出了一个简单的数值案例来说明所面临的问题和我们方法背后的想法，然后是一个实际案例来证明其在可靠性工程中的有用性。结果表明，与非理想情况下的现有研究相比，我们的方法在参数估计和可靠性评估方面具有一些优势，即先验有偏差和数据有限。这种方法可以深入了解系统/产品在其早期使用期间的可靠性评估，此时测试数据通常是有限的，而且先验信息总是不准确的。