A Review on the Method of Reliability Analysis of Networks with Emphasis on Lifeline Network Performance after Earthquake

Sufficient knowledge about the method of analyzing and reliability of network is essential to estimate the damage of systems and networks after earthquake. So, the method of reliability analysis networks is important and it is one of the aims of this study. A special characteristic of the current organization of the human life is the growing level of the interconnectivity. A tendency to increase in dimension and to aggregate in complex interconnected systems exists in economical, social, and technological structures. One important property of networks is that the connection between any two nodes of the networks can be typically reached through a number of redundant paths, thus making the connection basically reliable, and it makes them an advantaged structure both in natural and technological systems. Therefore, the reliability of networks has always been a main alarm since the earliest times of reliability engineering. Since the early 60s the exponential growth of the size and number of networks of all types has led many researchers to study the various characteristics, the topology, and the reliability of the networks. Now, the analysis of the network reliability is a major concern for the formation, validation and maintenance of many real systems such as communication, computer or electrical networks. The reliability of these complex systems is of increasing importance since the failure of some components may lead to catastrophic results.The failure of definite sets of components in the worst case may cause the failure of the network itself. In many real-life states, components and/or systems can be in one of more than two states (up and down). Systems that are characterized by different levels of performance are known as multi-state system (MSS).Power systems and computer systems are examples of MSS where the performance of the elements is characterized by generating capacity and data processing speed respectively. Most of reliability analysis and optimization models suppose that system is made of binarystate components, where the states are functioning and failure. Binary-state reliability models don’t allow to satisfactorily describing some aspects of the MSS as MSS operation processes, remaining resources, system state evolution, reasons of system failures and mechanisms of their prevention.The main difficulty in the MSS reliability analysis is the “dimension damnation” since each system element can have many different states(not only two states as the binary-state system). In this study, graphs, systems and binary decision diagram are introduced. Complex networks are described. Also, the specific properties of random networks and scale free networks are illustrated. Finally, weighted multi-state networks have been explained.