故障树、决策树与二元决策图：系统性比较
Fault Trees, Decision Trees, And Binary Decision Diagrams: A Systematic Comparison
AI总结：
本文针对可靠性工程中三类主流图模型对比不明确的问题，从用途、结构、分析方法等五个维度对故障树、决策树和二元决策图开展系统性比较，结合实例验证了三者的异同与优劣势，明确了模型间的转换关系与效率差异。
摘要：
在可靠性工程领域，我们需要厘清系统依赖关系、因果关联，识别关键组件，并分析这些组件如何引发故障。目前常用于实现上述目标的三类主流图模型分别是故障树（FTs）、决策树（DTs）和二元决策图（BDDs）。这类模型之所以得到广泛应用，是因为它们具备良好的可解释性，可作为不同背景利益相关方之间的沟通工具，同时能为决策流程提供支撑。此外，这类模型可通过计算可靠性指标、最小割集、逻辑规则以及展示依赖关系，帮助我们理解实际工程问题。然而，目前学界尚不清楚这三类图模型之间的对比情况。因此，本文的研究目标是通过系统性比较厘清三者的异同，比较维度包括：（1）用途与应用场景、（2）结构表示方式、（3）分析方法、（4）构建方式、（5）优势与局限性。此外，我们采用基于集装箱封条设计的贯穿性实例，展示三类模型的实际应用效果。研究结果表明，由于故障树、决策树和二元决策图的用途与应用领域各不相同，它们采用了不同的结构表示方式与分析方法，因此具备多样化的优势与局限性，而局限性可通过转换方法或扩展手段加以解决。具体结论包括：二元决策图可被视为二元决策树的紧凑表示形式，因为前者支持子节点共享，这使得二元决策图在表示逻辑规则时比二元决策树更高效。我们可以从二元决策图和决策树中提取割集，并通过（合取/析取）范式构建故障树，不过这种方式可能会得到次优的故障树结构。
英文摘要：
In reliability engineering, we need to understand system dependencies, cause-effect relations, identify critical components, and analyze how they trigger failures. Three prominent graph models commonly used for these purposes are fault trees (FTs), decision trees (DTs), and binary decision diagrams (BDDs). These models are popular because they are easy to interpret, serve as a communication tool between stakeholders of various backgrounds, and support decision-making processes. Moreover, these models help to understand real-world problems by computing reliability metrics, minimum cut sets, logic rules, and displaying dependencies. Nevertheless, it is unclear how these graph models compare. Thus, the goal of this paper is to understand the similarities and differences through a systematic comparison based on their (i) purpose and application, (ii) structural representation, (iii) analysis methods, (iv) construction, and (v) benefits & limitations. Furthermore, we use a running example based on a Container Seal Design to showcase the models in practice. Our results show that, given that FTs, DTs and BDDs have different purposes and application domains, they adopt different structural representations and analysis methodologies that entail a variety of benefits and limitations, the latter can be addressed via conversion methods or extensions. Specific remarks are that BDDs can be considered as a compact representation of binary DTs, since the former allows sub-node sharing, which makes BDDs more efficient at representing logical rules than binary DTs. It is possible to obtain cut sets from BDDs and DTs and construct a FT using the (con/dis)junctive normal form, although this may result in a sub-optimal FT structure.
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