Abstract
Dynamic Fault Trees (DFTs) are increasingly being used for modeling the failure behaviors of systems, particularly dynamic behaviors that cannot be captured using conventional combinatorial models. Traditionally, paper and pencil or simulation are used for the analysis of DFTs. While the former can provide generic expressions for the probability of failure, its results are prone to human errors. The latter method is based on sampling and the results are not guaranteed to be complete. Leveraging upon the expressive and sound nature of higher-order logic (HOL) theorem proving, it has been recently proposed for the analysis of DFTs algebraically. In this paper, we propose a novel methodology for the formal analysis of DFTs, based on the algebraic approach, while capturing both the qualitative and probabilistic aspects using theorem proving. In this paper, we further enrich the DFT library in HOL by providing the formalization of spare gates with a shared spare and the verification details of their probabilistic behavior. To demonstrate the utilization of our methodology, we apply it for the formal analysis of two safety-critical systems, namely, a drive-by-wire system and a cardiac assist system.
Highlights
Fault trees (FTs) have been widely used in modeling the causes of failure of systems [1]
In this paper, we proposed a novel methodology to conduct the formal analysis of Dynamic Fault Trees (DFTs) using higher-order logic (HOL) theorem proving
This methodology supports accurate qualitative and quantitative analyses of DFTs based on the soundness and expressive nature of HOL theorem proving
Summary
Fault trees (FTs) have been widely used in modeling the causes of failure of systems [1]. Leveraging upon the expressive and sound nature of HOL theorem proving, it has been recently proposed for the analysis of DFTs based on the algebraic approach, qualitatively [16] and quantitatively [17]. We propose a methodology to perform formal qualitative and probabilistic analyses based on the algebraic approach [9] using HOL theorem proving. Using HOL theorem proving, we have been able to identify a flaw in one of the simplification theorems that is used in the application section of the paper, which affects the integrity of the reported results This further strengthens our claim that it is necessary to formally verify the correctness of the algebraic approach to preserve the integrity of the analysis. The proposed methodology provides complete formal qualitative and probabilistic analyses in the form of generic expressions of probability of failure using HOL theorem proving. Both systems require sound analysis as any flaw in the analysis may lead to losses in lives
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call