Our research aims to investigate the relation between Physical Quantities and Reliability through the Topological Structure of the system. To do so, we study the Reliability of Simple Networks in the Form of Chains and Rings in this Thesis. These two forms represent the absence and presence of a periodic boundary condition, or in another word, whether a definite boundary exists.

We employ both analytical and numerical methods in this thesis. We set up a complete new Mathematical framework for study of network reliability under the concern of Fully Path-Connectedness. This Mathematical framework allows us to derive a general formula for network reliability and explain the difference between ring and chain structure. We are also able to prove one important feature of the Wheatsto...[ Read more ]

Our research aims to investigate the relation between Physical Quantities and Reliability through the Topological Structure of the system. To do so, we study the Reliability of Simple Networks in the Form of Chains and Rings in this Thesis. These two forms represent the absence and presence of a periodic boundary condition, or in another word, whether a definite boundary exists.

We employ both analytical and numerical methods in this thesis. We set up a complete new Mathematical framework for study of network reliability under the concern of Fully Path-Connectedness. This Mathematical framework allows us to derive a general formula for network reliability and explain the difference between ring and chain structure. We are also able to prove one important feature of the Wheatstone Bridge Chain and explain the configurational dependence of the reliability of the Wheatstone Bridge Ring.

Together with simulation results, we will show how symmetry can be related to the network reliability in this thesis. We will demonstrate a useful approximation method in ranking different networks according to their reliabilities. We will as well explain how phase transition-like behaviors can happen in networks.