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Dynamic and dependent tree theory (D<sup>2</sup>T<sup>2</sup>): A framework for the analysis of fault trees with dependent basic events

Andrews, John; Tolo, Silvia


Professor of Infrastructure Asset Management


Fault tree analysis remains the most commonly employed method, particularly in the safety critical industries, to predict the probability or frequency of system failures. Whilst it has its origins back in the 1960s, the assumptions employed in the majority of commercial fault tree analysis codes have not changed significantly since this time and restrict the ability of the method to represent features of the design, operation and maintenance of modern industrial systems. The inability to include general dependencies between the basic events, the requirement for invariant failure and repair rates, and the inability to account for complex maintenance strategies are major limitations. This paper proposes a new fault tree analysis framework which can overcome these restrictions. Whilst retaining the fault tree structure to express the causality of the system failure, the internal calculation method is updated by exploiting features of the Binary Decision Diagram, Stochastic Petri Net and Markov methods. The key elements of the D2T2 algorithm are described in detail and the framework demonstrated through application to a case study example of a pressure vessel cooling system.


Andrews, J., & Tolo, S. (2023). Dynamic and dependent tree theory (D2T2): A framework for the analysis of fault trees with dependent basic events. Reliability Engineering and System Safety, 230, Article 108959.

Journal Article Type Article
Acceptance Date Nov 4, 2022
Online Publication Date Nov 11, 2022
Publication Date Feb 1, 2023
Deposit Date Nov 8, 2022
Publicly Available Date Nov 12, 2023
Journal Reliability Engineering and System Safety
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 230
Article Number 108959
Keywords Industrial and Manufacturing Engineering; Safety, Risk, Reliability and Quality
Public URL
Publisher URL


This file is under embargo until Nov 12, 2023 due to copyright restrictions.

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