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Annual Symposium Reliability and Maintainability, 2004 - RAMS
The proposed tool, using a novel "compression algorithm" is capable of reducing any complicated seriesparallel system to a visible sequence of series and parallel blocks in a reliability block diagram (RBD) by first finding all existing paths, then algorithmically compressing all redundant component duplications and finally calculating an exact reliability and creating an encoding of the topology. A fast algorithm to perform state enumeration in a hybrid form assisted by the polish encoding approach on complex networks to compute the exact s-t reliability is in progress by the authors. The graphical screening ease and convenience of this algorithm is advantageous for planners and designers trying to improve system reliability by allowing a quick and efficient intervention that may be required at a dispatch center to observe routine operations and/or identify solution alternatives in case of a crisis. Note, s denotes the source and t denotes the target.
Frontiers in Science and Engineering, 2016
Several production systems either for goods or services can be modeled by a network where nodes are production centers, warehouses, distributions and others, and arcs represent the relationship between nodes. Nodes and arcs are often subjected to random failures that may result from several causes. These networks include one or more sources and one or more destinations. Given the stochastic nature of the failure, the reliability and the robustness of the network become an important criteria for safety, economical and environment reasons. Several methods based on graph theory and stochastic processes are proposed in the literature. The concepts of minimal paths set (MPS) and minimal cuts set (MCS) as well as decomposition techniques based on Bayes' theorem have been widely used. The performance of these methods is greatly affected by network size (number of nodes and arcs) and its density. Generally, except for special structure of some networks (e.g series, parallel, standby, etc.) there is no mathematical expression based on the reliability of its nodes and its arcs that has been proved compact for representing the expression of the reliability function of any network. This paper attempts to provide solutions to this problem by proposing and testing a unified approach based on MPS/MCS and Binary Decision Diagrams (BDD). This approach is illustrated by several simple examples. A tool has been developed to handle complex networks such as telecommunication networks and other network's tests published in the literature.
AIP Conference Proceedings, 2015
Reliability Block Diagrams (RBDs) allow us to model the failure relationships of complex systems and their sub-components and are extensively used for system reliability, availability, dependability and maintainability analyses of many engineering systems. Traditionally, Reliability Block Diagrams (RBD) are analyzed using paper-and-pencil proofs or computer simulations. Recently, formal techniques, including Petri Nets and higher-order-logic theorem proving, have been used for their analysis as well. In this paper, we provide a concise survey of these available RBD analysis techniques and compare them based on their accuracy, user friendliness and computational requirements.
2007
Dependability evaluation is an important, often indispensable, step in design and analyze (critical) systems, acquiring importance with the systems complexity growth. When the complexity of a system is high and/or increases, for example automizing or expanding some parts, dynamic effects, not present or manifested before, could arise or become significant in terms of reliability/availability. The system could be affected by common cause failures, the system components could interfere each other or could become inter/sequencedependent, effects due to load sharing arise and therefore should be considered, and so on. Moreover could be interesting to evaluate redundancy and maintenance policies. In those cases it is not possible to recur to notations as reliability block diagrams (RBD), fault trees (FT) or reliability graphs (RG) to represent the system, since the statistical independence assumption is not satisfied. Also more enhanced formalisms as dynamic FT (DFT) could not result adequate to the objective. To overcome those problems we developed a new formalism derived from RBD: the dynamic RBD (DRBD). In this paper we explain how to use the DRBD notation in system modeling and analysis, coming inside a methodology that, starting from the system structure, drives to the overall system availability evaluation following modeling and analysis phases. To do this we use an example drawn from literature, consisting of a multiprocessor distributed computing system. By this we also compare our approach with the DFT one.
2021
Reliability Block Diagrams (RBDs) are widely used in reliability engineering to model how the system reliability depends on the reliability of components or subsystems. In this paper, we present librbd, a C library providing a generic, efficient and open-source solution for time-dependent reliability evaluation of RBDs. The library has been developed as a part of a project for reliability evaluation of complex systems through a layered approach, combining different modeling formalisms and solution techniques at different system levels. The library achieves accuracy and efficiency comparable to, and mostly better than, those of other well-established tools, and it is well designed so that it can be easily used by other libraries and tools.
Quality and Reliability Engineering International, 2019
Reliability analysis of Infrastructure Networks (INs) is gaining recognition in the research literature. However, most of the work on reliability evaluation of INs have focused on simulation analysis and, therefore, unable to calculate the exact reliability. Additionally, these methods lack the capability of achieving a closer adherence to INs. The presented paper aims at filling these gaps by simplifying the process of computing the exact reliability of an IN through the decomposition of the network into a set of series and parallel configuration of its elements. In exemplifying the method, an illustrative example is presented and a brief discussion on the usefulness and limitation of the method is described.
1st IFAC Workshop on Dependable Control of Discrete Systems (2007), 2007
Many social, economical and technological structures can be abstracted in the form of networks where the vertices are the entities of the system and the edges the physical or relational links among them. One relevant property of networks that make them a preferential structure both in natural and technological systems is that the connection between any two nodes of the networks can be achieved through many redundant paths, thus making the connection intrinsically reliable. Network reliability is studied in this paper by resorting to different approaches making use of the BDD representation of Boolean functions. The related algorithms are presented and their merits and limits are briefly discussed.
IEEE Transactions on Industry Applications, 2004
This is one of a series of papers discussing the application and accuracy of different analysis techniques supporting the determination of industrial and commercial power system reliability and availability. There is a need recognized in the power industry to identify and utilize a standard tool, or a set of tools, to analyze the reliability of power systems. Historically, the results of applying different reliability methodologies and tools varied significantly, and comparisons were difficult. The Reliability Analysis Techniques Working Group of the Gold Book (IEEE Std. 493-1997) developed a standard network to enable comparison of analytical techniques. This paper describes the approach of simulations via reliability block diagrams as applied to the Gold Book standard network. Reliability indexes of the load points are presented, and are compared with ones obtained from other techniques in the series to determine the accuracy.
IFAC Proceedings Volumes, 2010
This paper presents an efficient approach that can be applied to solve the redundancy reliability allocation problem. The optimization problem considers optimization of the system design reliability (respectively: the cost of the allocation) subject to constraints on resources (target system reliability, costs and weights). The algorithm is based on three major steps that use-(1) a depth first search to determine 2-terminal reliability minimal paths, (2) a binary decision diagrams to compute the network reliability and (3) a procedure to find the solution to the optimizing problem. Examples for different networks are used to testify the usefulness of the method so we present some comparison tests
American Journal of Operations Research
The purpose of this paper is to propose a computational technique for evaluating the reliability of networks subject to stochastic failures. In this computation, a mathematical model is provided using a technique which incorporates the effect of the factoring decomposition theorem using polygonto-chain and series-parallel reductions. The algorithm proceeds by identifying iteratively one of seven polygons and when it is discovered, the polygon is immediately removed and replaced by a simple chain after having changed the individual values of the reliability of each edge and each node of the polygon. Theoretically, the mathematical development follows the results presented by Satyanarayana & Wood and Theologou & Carlier. The computation process is recursively performed and less constrained in term of execution time and memory space, and generates an exact value of the reliability.
Discrete Applied Mathematics, 1996
This paper presents an algorithm for computing the K-terminal reliability of undirected networks, i.e. the probability that a given set of vertices in the network are connected. when edges and nodes fail independently with known probabilities. This algorithm is based on a decomposition method introduced by Rosenthal. It consists in numbering the vertices of the graph so that the successive boundary sets are as small as possible and in evaluating the probabilities of appropriate classes of boundary sets. We show that for the all terminal reliability problem these classes are the partitions of the boundary sets and we describe them for the general problem. Our computational results are so conclusive that networks much largeIthan those presented before can now be treated.
International Journal of Distributed and Parallel systems, 2010
In this Paper we consider three different types of variable ordering; namely optimal ordering, good ordering and bad ordering for constructing the BDD of a given network by applying three different heuristics. This classification is based on the size of the BDD, because the size of the BDD strongly depends on the ordering of variables. After that we find the reliability of the given network by these different BDD. It is observed experimentally that the results (Reliability) of applying Classical Inclusionexclusion principle are the same as obtained by applying BDD for calculating reliability of a given network in each case. However the complexity of the BDD increases in bad ordering case.
The mathematical theory of reliability has grown out of the demand of modern technology and particularly out of the experience with complex systems. The main objective is to enhance the ability of such complex network systems. This work present an efficient algorithm, which is a novel approach to generate all the minimal paths of the general flow network based on the principle of backtracking. It is a general flow network because, the proposed approach can find the minimal paths for multiple sources and multiple sinks in the network. One can further evaluate the network reliability using any existing SDP (Sum of Disjoint Products) based approach.
Risk assessment of urban infrastructure networks under natural and man-made hazards is often performed by repeated computational simulations based on random samples of hazard intensities and corresponding component status. This sampling-based approach may prevent near-real-time application of probabilistic methods to hazard mitigation of infrastructure networks and risk-informed decision support. This paper proposes a non-sampling-based, multi-scale network reliability analysis approach based on the recently proposed matrix-based system reliability method. This approach accounts for the spatial correlation of hazard intensities and makes use of the disjoint cut sets or link sets identified by a state-of-the-art network analysis algorithm. The paper demonstrates the proposed approach through a case study of a Memphis Light, Gas and Water natural gas network under seismic hazard.
— A new method for calculating network reliability is presented in this paper. This method allows the analysis of complex communication networks by the use of multistage algorithm based on the hybrid combination of reduction technique and tie set methods. The algorithm begins with the application of reduction technique to simplify the network topology by elimination all series and parallel connection of communication links. The second stage is the application of an algorithm consisting of finding all tie-sets of the reduced network. The simplifications of the network in the first stage will affect positively the number and the complexity of tie sets, keeping the final result of the network reliability unchanged. Links probabilities are used to generate the network topologies with imperfect communication nodes, and bidirectional links which will yield to a more general situation. Algorithms and calculation are executed on MATLAB, where all the above assumptions are taken into account.
In this paper we propose an improved BDD approach to the network reliability analysis, that allows the user to compute an exact solution or an approximation based on reliability bounds when network complexity makes the former solution practically impossible. To this purpose, a new algorithm for encoding the connectivity graph on a Binary Decision Diagram (BDD) has been developed; it reduces the computation memory peak with respect to previous approaches based on the same type of data structure without increasing the execution time, and allows us also to derive from a subset of the minpaths/mincuts a lower/upper bound of the network reliability, so that the quality of the obtained approximation can be estimated. Finally, a fair and detailed comparison between our approach and another state of the art approach presented in the literature is documented through a set of benchmarks.
52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2011
Survivability, or the ability to deliver service in spite of multiple simultaneous faults caused by natural or hostile disruptions, is a desirable feature of any complex system. Our study is relevant to systems with sources (elements generating a quality of interest) and sinks (elements consuming this quantity). A key factor for such a system to survive is its topology, that is, the number of sources and sinks and their connections with one another. Previously, we developed a methodology for conducting the analysis of the system survivability due to its topology. However, the application of the analysis to real-life systems such as, for example, power systems, is a computational challenge. System topologies usually contain thousands of elements. The problem can be solved in principle by decomposing a topology with multiple sinks and multiple sources into a few sub-topologies with multiple sources and a single sink. An efficient computational procedure for the survivability analysis of a single-sink topology has already been developed in our previous studies. Two other steps that have yet to be developed are i) automatical transformation of a system diagram into a form suitable for the computational analysis and ii) automatical decomposition of a system with multiple sources and sinks into simpler sub-systems. The current paper reports on software development for converting a standard power system diagram into a structured adjacency matrix or list.
Network reliability evaluation techniques, e.g., path (cut) set techniques, factoring theorem based techniques etc., evaluate various network reliability measures based on different connectivity criterion of nodes, which is a NP hard problem. A little change in network layout requires repetition of the complete procedure. In this paper, a new approach based on path set technique is proposed. The proposed approach stores and process reliability expressions in terms of minimal path sets and disjoint sets using binary data structure. This paper proposes algorithms for modifying these sets with modifications in network layout. This paper also proposes a method to evaluate reliability defined on the basis of different node connectivity requirements.
IEEE Transactions on Reliability, 1976
Our algorithm has the following five advantages.
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