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In reliability engineering, we need to understand system dependencies,cause-effect relations, identify critical components, and analyze how theytrigger failures. Three prominent graph models commonly used for these purposesare fault trees (FTs), decision trees (DTs), and binary decision diagrams(BDDs). These models are popular because they are easy to interpret, serve as acommunication tool between stakeholders of various backgrounds, and supportdecision-making processes. Moreover, these models help to understand real-worldproblems by computing reliability metrics, minimum cut sets, logic rules, anddisplaying dependencies. Nevertheless, it is unclear how these graph modelscompare. Thus, the goal of this paper is to understand the similarities anddifferences through a systematic comparison based on their (i) purpose andapplication, (ii) structural representation, (iii) analysis methods, (iv)construction, and (v) benefits & limitations. Furthermore, we use a runningexample 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 andapplication domains, they adopt different structural representations andanalysis methodologies that entail a variety of benefits and limitations, thelatter can be addressed via conversion methods or extensions. Specific remarksare that BDDs can be considered as a compact representation of binary DTs,since the former allows sub-node sharing, which makes BDDs more efficient atrepresenting logical rules than binary DTs. It is possible to obtain cut setsfrom BDDs and DTs and construct a FT using the (con/dis)junctive normal form,although this may result in a sub-optimal FT structure.

Fault Trees, Decision Trees, And Binary Decision Diagrams: A Systematic Comparison