This project aims at exploring the failure probability of some classes of reliability systems. In particular, we consider systems composed by n disaggregated components, and assume that the failure of such systems occur when k components fail, the so-called k-out-of-n systems. We offer different frameworks by including components' heterogeneity and their relevance in leading to the failure of the system.
The analysis is carried out by adopting a multifocal approach. By one side, we offer a statistical perspective on systems failure, by including the presence of a dependence structure among the components of the systems. At this aim, we propose also the construction of suitable copulas for describing the interconnections among components¿ lifetimes. By the other side, we advance a game theory model to identify the conditions leading to the minimization of the failure probability of the systems. In doing so, we discuss the relevance of the components and the possibility of having strategic interactions among them.
The proposed methods are tested over high-quality empirical instances. Among them, we mention the paradigmatic case of the stability of the macroeconomic framework in the Eurozone context.
The project outlined above has relevant implications under a methodological perspective, by adding to game theory and reliability models. Moreover, it presents practical implications in the context of finance, engineering and social science.
In the context of k-out-of-n systems, we aim at developing novel frameworks, starting from the very recent contributions on the field discussed in the previous section. In particular, we include in the analysis of the reliability function of a system the heterogeneous relevance of its components. Moreover, we add to the theory of multi-level reliability systems, by identifying clusters of components playing a more relevant role in the different levels of failure. Importantly, the considered k-out-of-n systems are tested over relevant empirical instances, to describe the stability property of unified settings related to real-world contexts ¿ like the Eurozone or the stability of the interbanking network. The study of copulas when analysing multivariate survival times is an area of ongoing research; it is susceptible of several interesting results and extensions as far as both the theoretical formulation of the problem (including the issues in estimation) and the impact in applications are concerned.
Finally, the game theoretical models applied to reliability systems offer advancements under several viewpoints: the assessment of relevance of the failure of the single components, an improvement on the discussion concerning the system structures, and their related heterogeneity.
REFERENCES (see previous sections)
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