A literature review on network reliability analysis and its engineering applications

The applications of networks can be observed in numerous engineering realms mainly computers and communication, transportation, electric transmission and oil and gas distribution. Estimating the reliability of such networks is a critical task for the well-being of society as well as a nation. The paradigm of network reliability has evolved considerably over the past few decades. The purpose of this article is to present the developments in network reliability domain in a laconic manner. This paper discusses the various metrics used to evaluate network connectivity along with their mathematical backgrounds. The various algorithms namely State Enumeration, Sum of disjoint product, Minimal Cut Set, Factoring theorem, Cellular Automata, Subset Simulation, Percolation theory, Binary Decision Diagrams, and Universal Generating Functions are enumerated in this review study. The application part of algorithms with their advantages, limitations and scope are presented. Finally, the methodologies used for assessment of network reliability are discussed. This article aims at providing a holistic view of the network reliability practices, which may prove to be helpful for researchers across the globe.

Dynamic Fault Tree Analysis Based on Dynamic Uncertain Causality Graph

Dynamic Fault Tree (DFT) has drawn attention from comprehensive industrial systems in recent years. Many analytical approaches are developed to analyze DFT, such as Markov Chain based method, Inclusion-Exclusion Rule based method, and Sum-of-Disjoint-Product theory based method. Novel methods such as Bayesian Network and Petri Net are also used to solve DFT. However, Basic events are usually assumed unrepairable and are restricted to specific probabilistic distributions. And some methods may suffer from combination explosion. This paper applies Dynamic Uncertain Causality Graph (DUCG) to analyze DFT to overcome the aforementioned issues. DUCG is a newly proposed Probabilistic Graphic Model for large complex industrial systems which allows for dynamics, uncertainties and logic cycles. The DUCG based methodology can be summarized as event mapping, logical mapping, and numerical mapping. This paper studies how to map the PAND, FDEP, SEQ AND SPARE sequential logic gates into equivalent representations in DUCG. With the DUCG representation mode, one can analyze DFT with algorithms in DUCG. Future work will be done on benchmark tests and on software development.

On the Disjoint Product of Irreducible Representations of the Symmetric Group

The results of the present paper can be interpreted (a) in terms of the theory of the representations of the symmetric group, or (b) in terms of the corresponding theory of the full linear group. In the latter connection they give a solution to the problem of the expression of an invariant matrix of an invariant matrix as a sum of invariant matrices, in the sense of Schur's Dissertation. D. E. Littlewood has pointed out the significance of this problem for invariant theory and has attacked it via Schur functions, i.e. characters of the irreducible representations of the full linear group. We shall confine our attention here to the interpretation (a).