Reliability Analysis of Complex Multi-State System Based on Universal Generating Function and Bayesian Network

TL;DR

The paper addresses the challenge of reliability analysis for complex multi-state systems (MSS) with unclear or implicit interdependencies. It proposes UGF-BN, a hybrid framework that uses the Universal Generating Function (UGF) to efficiently model bottom components and Bayesian Network (BN) inference to handle structure-function relationships lacking explicit expressions, ultimately yielding $R_{system}$. The work demonstrates two key contributions: (i) substantial computational savings over pure BN for large MSS and (ii) integration of UGF-BN into aircraft reliability-based design optimization under mass, power, and cost budgets, validated by two case studies. The results show accurate reliability estimates and significant design improvements, highlighting the practical impact for scalable, uncertainty-aware reliability analysis in aerospace systems.

Abstract

In the complex multi-state system (MSS), reliability analysis is a significant research content, both for equipment design, manufacturing, usage and maintenance. Universal Generating Function (UGF) is an important method in the reliability analysis, which efficiently obtains the system reliability by a fast algebraic procedure. However, when structural relationships between subsystems or components are not clear or without explicit expressions, the UGF method is difficult to use or not applicable at all. Bayesian Network (BN) has a natural advantage in terms of uncertainty inference for the relationship without explicit expressions. For the number of components is extremely large, though, it has the defects of low efficiency. To overcome the respective defects of UGF and BN, a novel reliability analysis method called UGF-BN is proposed for the complex MSS. In the UGF-BN framework, the UGF method is firstly used to analyze the bottom components with a large number. Then probability distributions obtained are taken as the input of BN. Finally, the reliability of the complex MSS is modeled by the BN method. This proposed method improves the computational efficiency, especially for the MSS with the large number of bottom components. Besides, the aircraft reliability-based design optimization based on the UGF-BN method is further studied with budget constraints on mass, power, and cost. Finally, two cases are used to demonstrate and verify the proposed method.

Figures (16)

• Figure 1: An aircraft information transmission system structure.
• Figure 2: Digraph from $X$ to $Y$.
• Figure 3: A simple case of the BN.
• Figure 4: Main strategies of the UGF-BN method.
• Figure 5: The construction of the hierarchical system.