Fault trees (FTs) are among the most prominent formalisms for reliability analysis of technical systems. Dynamic FTs extend FTs with support for expressing dynamic dependencies among components. The standard analysis vehicle for DFTs is state-based, and treats the model as a continuous-time Markov chain (CTMC). This is not always possible, as we will explain, since some DFTs allow multiple interpretations. This paper introduces a rigorous semantic interpretation of DFTs. The semantics is defined in such a way that the semantics of a composite DFT arises in a transparent manner from the semantics of its components. This not only eases the understanding of how the FT building blocks interact. It is also a key to alleviate the state explosion problem. By lifting a classical aggregation strategy to our setting, we can exploit the DFT structure to build the smallest possible Markov chain representation of the system. The semantics—as well as the aggregation and analysis engine is implemented in a tool, called CORAL. We show by a number of realistic and complex systems that this methodology achieves drastic reductions in the state space.

This paper proposes a formally well-rooted and extensible framework for dependability evaluation: Arcade (architectural dependability evaluation). It has been designed to combine the strengths of previous approaches to the evaluation of dependability. A key feature is its formal semantics in terms of input/output-interactive Markov chains, which enables both compositional modeling and compositional state space generation and reduction. The latter enables great computational reductions for many models. The Arcade approach is extensible, hence adaptable to new circumstances or application areas. The paper introduces the new modeling approach, discusses its formal semantics and illustrates its use with two case studies.

This paper discusses the requirements that a suitable formalism for dependability modeling/evaluation should possess. We also discuss the outline of Arcade, an architectural dependability formalism that we are developing.

In the above titled paper (ibid., vol 55, no. 1, pp. 86-97, Mar 06), a few errors and typos occurred. The corrections are presented here.

Dynamic fault trees (DFT) extend standard fault trees by allowing the modeling of complex system components' behaviors and interactions. Being a high level model and easy to use, DFT are experiencing a growing success among reliability engineers. Unfortunately, a number of issues still remains when using DFT. Briefly, these issues are (1) a lack of formality (syntax and semantics), (2) limitations in modular analysis and thus vulnerability to the state-space explosion problem, and (3) lack in modular model-building. We use the input/output interactiveMarkov chain (I/O-IMC) formalism to analyse DFT. I/O-IMC have a precise semantics and are an extension of continuous-time Markov chains with input and output actions. In this paper, using the I/OI-MC framework, we address and resolve issues (2) and (3) mentioned above. We also show, through some examples, how one can readily extend the DFT modeling capabilities using the I/O-IMC framework.

We present a continuous-time Bayesian network (CTBN) framework for dynamic systems reliability modeling and analysis. Dynamic systems exhibit complex behaviors and interactions between their components; where not only the combination of failure events matters, but so does the sequence ordering of the failures. Similar to dynamic fault trees, the CTBN framework defines a set of 'basic' BN constructs that capture well-defined system components' behaviors and interactions. Combining, in a structured way, the various 'basic' Bayesian network constructs enables the user to construct, in a modular and hierarchical fashion, the system model. Within the CTBN framework, one can perform various analyses, including reliability, sensitivity, and uncertainty analyses. All the analyses allow the user to obtain closed-form solutions.