The structure function describes the functioning of a system dependent on the states of its components, and is central to theory of system reliability. Hasse diagram is a mathematical diagram used to represent a finite partially ordered set, in the form of a graph of its transitive reduction. Representing the system state on the Hasse diagram, we obtain an ordered graph of system states. The monotony property of the structure function of coherent systems allows us to automatically obtain this ordered graph of system states from the only knowledge of the minimal path-sets or minimal cut-sets. This lecture will present how a minimal disjoint form of the system structure function and how the analytical expression of system reliability can be computed by relying on graphs issued from Hasse diagram. This approach allows us to directly obtain the reliability expression for both types of systems: coherent or non-coherent. We will also present how such graphs can be used in evaluation of importance of system components.