Generic methodology for the probabilistic reliability assessment of some structural properties: a graph theoretical approach

The graphical characterisation of many important structural properties, such as controllability, observability, diagnosability of many kinds of structured systems, uses mainly four types of elementary graphical conditions: connectivity, complete matching, linking and distance conditions. Since structural properties depend on different associations of elementary conditions, it is interesting to study elementary conditions. This paper is the first part of this global approach based on elementary graphical conditions and we choose to study the so-called connectivity and complete matching conditions. Starting from the graphical representation associated with a system, the paper provides Boolean expressions of the connectivity and complete matching conditions based on the edges validity, which can be linked to the physical components operating state. These expressions can then be used to define and compute the reliability of a structural property knowing the reliability of the system physical components. This knowledge can be important during both conception and exploitation stages. The proposed methods are quite intuitive and simple to implement and have basically polynomial complexity orders. This makes our approach well suited to analyse large-scale systems.