In engineering, there exist multiple priors about system and subsystems uncertainties, which should be integrated properly to analyze the system reliability. In the past research, an iterative updating procedure based on Bayesian Melding Method (I-BMM) was developed to merge and update multiple priors for the double-level system. However, the in-depth study in this paper shows that the original iterative procedure has no effect on the prior updating. Thus it is proposed that only a single BMM iteration process is needed following the original prior integration and updating formulation. BMM involves the sampling procedure for the probability density function (PDF) updating, wherein it is generally difficult to define the sampling number properly for obtaining accurate priors. To address this problem, a sequential prior integration and updating framework based on the original single BMM iteration process (S-BMM) is developed in this paper. In each cycle of prior updating, the sample number is sequentially added, and the difference between prior distributions obtained in the two consecutive cycles is measured with the symmetric Kullback-Leibler Divergence (SKLD). The sequential procedure is continued until the convergence to the accurate updated prior. The S-BMM framework for double-level systems is further extended for multi-level systems. Situations with some missing subsystem or component priors are also discussed. Finally, two numerical examples and one satellite engineering case are used to demonstrate and verify the proposed algorithms.

在工程中，存在关于系统和子系统不确定性的多个先验知识，应该对其进行适当集成以分析系统可靠性。在过去的研究中，开发了一种基于贝叶斯融合方法（I-BMM）的迭代更新程序来合并和更新双层系统的多个先验。但是，本文的深入研究表明，原始的迭代过程对先前的更新没有影响。因此，提出了在原始的先前集成和更新公式之后仅需要单个BMM迭代过程。BMM涉及用于概率密度函数（PDF）更新的采样过程，其中通常很难正确定义采样数以获取准确的先验。为了解决这个问题，本文基于原始的单个BMM迭代过程（S-BMM），开发了一个顺序的先验集成和更新框架。在每个先验更新周期中，依次添加样本数量，并使用对称的Kullback-Leibler发散度（SKLD）测量两个连续周期中获得的先验分布之间的差异。继续顺序过程，直到收敛到准确的更新先验为止。双层系统的S-BMM框架进一步扩展为多层系统。还讨论了子系统或组件先验缺失的情况。最后，使用两个数值示例和一个卫星工程案例来论证和验证所提出的算法。在每个先验更新周期中，将样本数量顺序相加，并使用对称的Kullback-Leibler发散度（SKLD）测量两个连续周期中获得的先验分布之间的差异。继续顺序过程，直到收敛到准确的更新先验为止。双层系统的S-BMM框架进一步扩展为多层系统。还讨论了子系统或组件先验缺失的情况。最后，使用两个数值示例和一个卫星工程案例来论证和验证所提出的算法。在每个先验更新周期中，将样本数量顺序相加，并使用对称的Kullback-Leibler发散度（SKLD）测量两个连续周期中获得的先验分布之间的差异。继续顺序过程，直到收敛到准确的更新先验为止。双层系统的S-BMM框架进一步扩展为多层系统。还讨论了子系统或组件先验缺失的情况。最后，使用两个数值示例和一个卫星工程案例来论证和验证所提出的算法。继续进行顺序过程，直到收敛到准确的更新先验为止。双层系统的S-BMM框架进一步扩展为多层系统。还讨论了子系统或组件先验缺失的情况。最后，使用两个数值示例和一个卫星工程案例来论证和验证所提出的算法。继续进行顺序过程，直到收敛到准确的更新先验为止。双层系统的S-BMM框架进一步扩展为多层系统。还讨论了子系统或组件先验缺失的情况。最后，使用两个数值示例和一个卫星工程案例来论证和验证所提出的算法。