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

TL;DR

This paper systematically compares fault trees, decision trees, and binary decision diagrams in reliability engineering, highlighting their differences, similarities, and trade-offs through a practical example and analysis of their structures and applications.

Contribution

It provides a comprehensive comparison of FTs, DTs, and BDDs, clarifying their purposes, structures, and analysis methods, and discusses how to convert or extend them to address limitations.

Findings

BDDs are more efficient than binary decision trees due to sub-node sharing.

Cut sets can be derived from BDDs and DTs for reliability analysis.

Fault trees can be constructed from BDDs and DTs using normal forms, though sub-optimal.

Abstract

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.