Bayesian assessment of network reliability

The recent technological advances in communications, manufacturing, and transportation systems have made networks the mainstay of modern life. Consequently, the reliability of networks has become an important issue and much progress has been made in its assessment. However, the state of the art here suffers from a serious limitation. It assumes that the underlying node and arc probabilities are known with certainty. The purpose of this paper is to rectify this shortcoming and to discuss, by way of a review, issues that have not been previously articulated. To accomplish our goal, we undertake three tasks. The first is to develop a joint prior distribution for the reliabilities of the individual components. This distribution is to be denned on the unit hypercube and should make provision for the incorporation of dependencies. Several strategies for specifying such a prior distribution are proposed. The second task is to generate samples from either the prior distribution or the resulting posterior distribution that is obtained when data from tests on the components is available. Because of the high dimensionality of the prior, or the posterior, this task is best accomplished via simulation techniques such as Gibbs sampling. The third task pertains to simulating the reliability of the network by using the samples obtained from the second task as inputs to an algorithm for network reliability calculations. The entire exercise of assessing network reliability is therefore computer intensive. The same is also true of fault tree analysis.