Decision Diagram Algorithms to Extract Minimal Cutsets of Finite Degradation Models

Abstract

In this article, we propose decision diagram algorithms to extract minimal cutsets of finite degradation models. Finite degradation models generalize and unify combinatorial models used to support probabilistic risk, reliability and safety analyses (fault trees, attack trees, reliability block diagrams…). They formalize a key idea underlying all risk assessment methods: states of the models represent levels of degradation of the system under study. Although these states cannot be totally ordered, they have a rich algebraic structure that can be exploited to extract minimal cutsets of models, which represent the most relevant scenarios of failure. The notion of minimal cutsets we introduce here generalizes the one defined for fault trees. We show how algorithms used to calculate minimal cutsets can be lifted up to finite degradation models, thanks to a generic decomposition theorem and an extension of the binary decision diagrams technology. We discuss the implementation and performance issues. Finally, we illustrate the interest of the proposed technology by means of the use case stemmed from the oil and gas industry.