Yes / Over the years, several approaches have been developed for the quantitative analysis of dynamic fault trees (DFTs). These approaches have strong theoretical and mathematical foundations; however, they appear to suffer from the state-space explosion and high computational requirements, compromising their efficacy. Modularisation techniques have been developed to address these issues by identifying and quantifying static and dynamic modules of the fault tree separately by using binary decision diagrams and Markov models. Although these approaches appear effective in reducing computational effort and avoiding state-space explosion, the reliance of the Markov chain on exponentially distributed data of system components can limit their widespread industrial applications. In this paper, we propose a hybrid modularisation scheme where independent sub-trees of a DFT are identified and quantified in a hierarchical order. A hybrid framework with the combination of algebraic solution, Petri Nets, and Monte Carlo simulation is used to increase the efficiency of the solution. The proposed approach uses the advantages of each existing approach in the right place (independent module). We have experimented the proposed approach on five independent hypothetical and industrial examples in which the experiments show the capabilities of the proposed approach facing repeated basic events and non-exponential failure distributions. The proposed approach could provide an approximate solution to DFTs without unacceptable loss of accuracy. Moreover, the use of modularised or hierarchical Petri nets makes this approach more generally applicable by allowing quantitative evaluation of DFTs with a wide range of failure rate distributions for basic events of the tree. / This work was supported in part by the Dependability Engineering Innovation for Cyber Physical Systems (CPS) (DEIS) H2020 Project under Grant 732242, and in part by the LIVEBIO: Light-weight Verification for Synthetic Biology Project under Grant EPSRC EP/R043787/1.

Yes / Fault tree analysis (FTA) is a powerful technique that is widely used for evaluating system safety and reliability. It can be used to assess the effects of combinations of failures on system behaviour but is unable to capture sequence dependent dynamic behaviour. A number of extensions to fault trees have been proposed to overcome this limitation. Pandora, one such extension, introduces temporal gates and temporal laws to allow dynamic analysis of temporal fault trees (TFTs). It can be easily integrated in model-based design and analysis techniques. The quantitative evaluation of failure probability in Pandora TFTs is performed using exact probabilistic data about component failures. However, exact data can often be difficult to obtain. In this paper, we propose a method that combines expert elicitation and fuzzy set theory with Pandora TFTs to enable dynamic analysis of complex systems with limited or absent exact quantitative data. This gives Pandora the ability to perform quantitative analysis under uncertainty, which increases further its potential utility in the emerging field of model-based design and dependability analysis. The method has been demonstrated by applying it to a fault tolerant fuel distribution system of a ship, and the results are compared with the results obtained by other existing techniques.

Yes / Fault Tree Analysis (FTA) is a well-established and well-understood technique, widely used for dependability evaluation of a wide range of systems. Although many extensions of fault trees have been proposed, they suffer from a variety of shortcomings. In particular, even where software tool support exists, these analyses require a lot of manual effort. Over the past two decades, research has focused on simplifying dependability analysis by looking at how we can synthesise dependability information from system models automatically. This has led to the field of model-based dependability analysis (MBDA). Different tools and techniques have been developed as part of MBDA to automate the generation of dependability analysis artefacts such as fault trees. Firstly, this paper reviews the standard fault tree with its limitations. Secondly, different extensions of standard fault trees are reviewed. Thirdly, this paper reviews a number of prominent MBDA techniques where fault trees are used as a means for system dependability analysis and provides an insight into their working mechanism, applicability, strengths and challenges. Finally, the future outlook for MBDA is outlined, which includes the prospect of developing expert and intelligent systems for dependability analysis of complex open systems under the conditions of uncertainty.

Yes / Dynamic systems exhibit time-dependent behaviours and complex functional dependencies amongst their components. Therefore, to capture the full system failure behaviour, it is not enough to simply determine the consequences of different combinations of failure events: it is also necessary to understand the order in which they fail. Pandora temporal fault trees (TFTs) increase the expressive power of fault trees and allow modelling of sequence-dependent failure behaviour of systems. However, like classical fault tree analysis, TFT analysis requires a lot of manual effort, which makes it time consuming and expensive. This in turn makes it less viable for use in modern, iterated system design processes, which requires a quicker turnaround and consistency across evolutions. In this paper, we propose for a model-based analysis of temporal fault trees via HiP-HOPS, which is a state-of-the-art model-based dependability analysis method supported by tools that largely automate analysis and optimisation of systems. The proposal extends HiP-HOPS with Pandora, Petri Nets and Bayesian Networks and results to dynamic dependability analysis that is more readily integrated into modern design processes. The effectiveness is demonstrated via application to an aircraft fuel distribution system. / Partly funded by the DEIS H2020 project (Grant Agreement 732242).