Reliability Block Diagrams (RBDs) are widely used in reliability engineering to model how the system reliability depends on the reliability of components or subsystems. In this paper, we present librbd, a C library providing a generic, efficient and open-source solution for time-dependent reliability evaluation of RBDs. The library has been developed as a part of a project for reliability evaluation of complex systems through a layered approach, combining different modeling formalisms and solution techniques at different system levels. The library achieves accuracy and efficiency comparable to, and mostly better than, those of other well-established tools, and it is well designed so that it can be easily used by other libraries and tools.

Technological advances in modern Train Control Systems (TCSs) promise to improve dependability of railway transportation in terms of safety, availability, and capacity, notably by employing novel distancing policies such as Moving Block (MB) signaling and Virtual Coupling (VC), fueled by advanced train localization methods such as satellite positioning. At the same time, these technological advances raise notable concerns about the effects that uncertainty in critical TCS parameters (such as train position and speed) may have on dependability-related attributes. Recently, various approaches have been proposed to characterize such effects through quantitative measures, leveraging formal stochastic modeling and evaluation of the TCS behavior. In this paper, we illustrate the results of a systematic review of the literature on quantitative evaluation of dependability-related attributes of TCSs under uncertainty on vital parameters. Specifically, we have finally selected 42 relevant papers, published between 2011 and 2023, that succeed in giving, through an empirical perspective and classification, a comprehensive view of current research and practice in quantitative dependability assessment of TCSs.

We evaluate a stochastic upper bound on the response time Probability Density Function (PDF) of complex workflows through an efficient and accurate compositional approach. Workflows consist of activities having generally distributed stochastic durations with bounded supports, composed through sequence, choice/merge, and balanced/unbalanced split/join operators, possibly breaking the structure of well-formed nesting. Workflows are specified using a formalism defined in terms of Stochastic Time Petri Nets that permits decomposition into a hierarchy of subworkflows with positively correlated response times, guaranteeing that a stochastically larger end-to-end response time PDF is obtained when intermediate results are approximated by stochastically larger PDFs and when dependencies are simplified by replicating activities appearing in multiple subworkflows. In particular, an accurate stochastically larger PDF is obtained by combining shifted truncated Exponential terms with positive or negative rates. Experiments are performed on sets of manually and randomly generated models with increasing complexity, illustrating under which conditions different decomposition heuristics work well in terms of accuracy and complexity and showing that the proposed approach outperforms simulation having the same execution time.