An efficient algorithm for computing exact system and survival signatures of K-terminal network reliability

An efficient algorithm is presented for computing exact system and survival signatures of K-terminal reliability in undirected networks with unreliable edges. K-terminal reliability is defined as the probability that a subset K of the network nodes can communicate with each other. Signatures have several advantages over direct reliability calculation such as enabling certain stochastic comparisons of reliability between competing network topology designs, extremely fast repeat computation of network reliability for different edge reliabilities and computation of network reliability when failures of edges are exchangeable but not independent. Existing methods for computation of signatures for K-terminal network reliability require derivation of cut-sets or path-sets which is only feasible for small networks due to the computational expense. The new algorithm utilises binary decision diagrams, boundary set partition sets and simple array operations to efficiently compute signatures through a factorisation of the network edges. The performance and advantages of the algorithm are demonstrated through application to a set of benchmark networks and a sensor network from an underground mine

Reliability evaluation of a multi-state system with dependent components and imprecise parameters: A structural reliability treatment

Reliability evaluation of a multi-state system (MSS) with dependent components makes much practical sense because the independent identical assumption (i.i.d.) assumption between different components is sometimes impractical in the context of real engineering cases. The task becomes more challenging if imprecision gets involved due to the pervasive uncertainty. The loss of monotony resulting from the introduction of imprecise parameters makes many analytical reliability methods not applied. To address this challenge, in this paper, we develop a survival signature-based reliability framework for an MSS taking into account both dependence and uncertainty. In our framework, the survival function is derived through some unique structural reliability treatments. Vine copula and imprecise probability are integrated and embedded within the framework to address the case that dependence and imprecision simultaneously appear. Implementation-wise, two numerical simulation algorithms are developed to address some complicated cases in which the analytical solution is not available. For demonstration and validation, both the numerical case and application examples are presented. The results show the superiority of the proposed method and its potential in real engineering use

Marginal and joint reliability importance based on survival signature

Marginal and joint reliability importance measures have been found to be useful in optimal system design. Various importance measures have been defined and studied for a variety of system models. The results in the literature are mostly based on the assumption that the components within the system are independent or identical. The present paper is concerned with computation of marginal and joint reliability importance for a coherent system that consists of multiple types of dependent components. In particular, by utilizing the concept of survival signature, expressions for marginal and joint reliability importance measures are presented. We also introduce reliability importance for a system of which only the survival signature is known, which therefore can be regarded to be a black box system