Connectivity condition for structural properties using a graph theoretical approach: Probabilistic reliability assessment

In a structured system graphically represented, the satisfaction of structural properties depends on graphical conditions. Among these conditions, we choose to study one of the most commonly used conditions, the so-called connectivity condition. The validity of this condition depends on the validity of some edges in the system graphical representation. The corresponding edges reflect the operating state of the physical system components. To study the validity of the connectivity condition, this paper describes a methodology which provides a Boolean expression of the connectivity condition based on the components operating state. As an application of the proposed Boolean expression, we can define the reliability characteristics of the connectivity condition and for how much time it remains satisfied knowing the reliability characteristics of the system components.