A Monte-Carlo simulation approach for approximating multi-state two-terminal reliability

This paper describes a Monte-Carlo (MC) simulation methodology for estimating the reliability of a multi-state network. The problem under consideration involves multi-state two-terminal reliability (M2TR) computation. Previous approaches have relied on enumeration or on the computation of multi-state minimal cut vectors (MMCV) and the application of inclusion/exclusion formulae. This paper discusses issues related to the reliability calculation process based on MMCV. For large systems with even a relatively small number of component states, reliability computation can become prohibitive or inaccurate using current methods. The major focus of this paper is to present and compare a new MC simulation approach that obtains accurate approximations to the actual M2TR. The methodology uses MC to generate system state vectors. Once a vector is obtained, it is compared to the set of MMCV to determine whether the capacity of the vector satisfies the required demand. Examples are used to illustrate and validate the methodology. The estimates of the simulation approach are compared to exact and approximation procedures from solution quality and computational effort perspectives. Results obtained from the simulation approach show that for relatively large networks, the maximum absolute relative error between the simulation and the actual M2TR is less than 0.9%, yet when considering approximation formulae, this error can be as large as 18.97%. Finally, the paper discusses that the MC approach consistently yields accurate results while the accuracy of the bounding methodologies can be dependant on components that have considerable impact on the system design.     

Confidence bounds for the reliability of binary capacitated two-terminal networks

Binary capacitated two-terminal reliability at demand level d (2TR_d) is defined as the probability that network capacity, generated by binary capacitated components, between specified source and sink nodes is greater than or equal to a demand of d units. For the components that comprise these networks, reliability estimates are usually obtained from some source of testing. For these estimates and depending on the type of testing, there is an associated uncertainty that can significantly affect the overall estimation of 2TR_d. That is, an accurate estimate of 2TR_d is highly dependent on the uncertainty associated to the reliability of the network components. Current methods for the estimation of network reliability and associated uncertainty are restricted to the case where the network follows a series-parallel architecture and the components are binary and non-capacitated. For different capacitated network designs, an estimate on 2TR_d can only be approximated for specific scenarios. This paper presents a bounding approach for 2TR_d by explaining how component reliability and associated uncertainty impact estimates at the network level. The proposed method is based on a structured approach that generates a α-level confidence interval (CI) for binary capacitated two-terminal network reliability. Simulation results on different test networks show that the proposed methods can be used to develop very accurate bounds of two-terminal network reliability.     

网络系统可靠性近似估算方法的对比研究

在讨论了网络系统可靠性计算难题的基础上，以满足工程实际的精度需要并减少分析计算工作量为目标，对现有的4种近似估算网络系统可靠性的方法进行了分析，指出了各种方法产生误差的原因，定性分析了有关方法为减少误差所采取措施的合理性。针时2种不同复杂程度的典型网络系统，通过数值算例，给出了单元可靠度不同情形下的系统可靠度计算值；与精确算法时比之后，得到了量化的误差．基于对各方法的工作量和误差的综合分析，给出了具有工程指导意义的建议．     

Multistate-node acyclic networks reliability evaluation based on MC

A multistate-node acyclic network (MNAN) is a generalization of the tree-structured multistate-node system that does not satisfy the flow conservation law. The current known existing methods used to evaluate MNAN reliability are based on the minimal tree (MT) set. Instead of using the MT, an intuitive algorithm was developed in this to find the minimal cut (MC) set. The MNAN reliability can then be computed in terms of MCs. The proposed algorithm is simpler and more efficient compared to the best-known existing methods. The computational complexity of the proposed algorithm is analyzed and compared with the best-known existing methods. One example is used to show how all MCs are generated using the proposed algorithm. The corresponding reliabilities in this example are computed.     

Reliability graph with general gates: an intuitive and practical method for system reliability analysis

In this paper, we propose an intuitive and practical method for system reliability analysis. Among the existing methods for system reliability analysis, reliability graph is particularly attractive due to its intuitiveness, even though it is not widely used for system reliability analysis. We provide an explanation for why it is not widely used, and propose a new method, named reliability graph with general gates, which is an extension of the conventional reliability graph. An evaluation method utilizing existing commercial or free software tools are also provided. We conclude that the proposed method is intuitive, easy-to-use, and practical while as powerful as fault tree analysis, which is currently the most widely used method for system reliability analysis.     

自组织网络的可靠性评估算法研究

网络的可靠性是网络性能评估指标的一个方面,他对于网络系统级的性能评估有重要意义。本文从网络可靠性的概念、可靠性分析角度介绍了三种自组织网络的可靠性评估算法:基于跳面节点的可靠性算法、可靠性的上下界估计算法和经验值估计算法的原理和特点,然后介绍了网络性能评估可靠性算法中的一种新的研究方向———效能系数评估法。     

事故树在炸药库管理上的应用

炸药库爆炸事故的频频发生,给国家带来了巨大损失.结合实例,采用事故树分析法(FTA)对某炸药库的爆炸事件作了定性分析,确定了引起项上事件的各个基本事件,构造了事故树和成功树,计算得出22个最小割集和5个最小径集,找出发生爆炸事故的可能原因和主要影响因素,并根据分析结果指出炸药库在管理上存在的缺陷,提出了相应的安全管理措施.对实施炸药库的安全管理具有参考价值.     

Identification of the electrical parameters of the passive two-terminal equivalent circuits of investigated objects

A method of constructing the topology of passive two-terminal equivalent circuits of investigated object on the basis of information on the frequency dependence of the active electric power dissipated in it is proposed. It is shown that using this method one can design data-measuring systems which enable the equivalent circuit of investigated objects to be synthesized. __________ Translated from Izmeritel’naya Tekhnika, No. 11, pp. 48–50, November, 2007.     

An evaluation of the multi-state node networks reliability using the traditional binary-state networks reliability algorithm

A system where the components and system itself are allowed to have a number of performance levels is called the Multi-state system (MSS). A multi-state node network (MNN) is a generalization of the MSS without satisfying the flow conservation law. Evaluating the MNN reliability arises at the design and exploitation stage of many types of technical systems. Up to now, the known existing methods can only evaluate a special MNN reliability called the multi-state node acyclic network (MNAN) in which no cyclic is allowed. However, no method exists for evaluating the general MNN reliability. The main purpose of this article is to show first that each MNN reliability can be solved using any the traditional binary-state networks (TBSN) reliability algorithm with a special code for the state probability. A simple heuristic SDP algorithm based on minimal cuts (MC) for estimating the MNN reliability is presented as an example to show how the TBSN reliability algorithm is revised to solve the MNN reliability problem. To the author's knowledge, this study is the first to discuss the relationships between MNN and TBSN and also the first to present methods to solve the exact and approximated MNN reliability. One example is illustrated to show how the exact MNN reliability is obtained using the proposed algorithm.     

A simple MC-based algorithm for evaluating reliability of stochastic-flow network with unreliable nodes

A MP/minimal cutset (MC) is a path/cut set such that if any edge is removed from this path/cut set, then the remaining set is no longer a path/cut set. An intuitive method is proposed to evaluate the reliability in terms of MCs in a stochastic-flow network subject to both edge and node failures under the condition that all of the MCs are given in advance. This is an extension of the best of known algorithms for solving the d-MC (a special MC but formatted in a system-state vector, where d is the lower bound points of the system capacity level) problem from the stochastic-flow network without unreliable nodes to with unreliable nodes by introducing some simple concepts. These concepts were first developed in the literature to implement the proposed algorithm to reduce the number of d-MC candidates. This method is more efficient than the best of known existing algorithms regardless if the network has or does not have unreliable nodes. Two examples are illustrated to show how the reliability is determined using the proposed algorithm in the network with or without unreliable nodes. The computational complexity of the proposed algorithm is analyzed and compared with the existing methods.     

Local-area network reliability models

This paper describes analyses of reliabilities of local area networks (LANs) designed according to the most common IEEE 802 standards: the token ring architecture (IEEE 802.5, basically the IBM token ring architecture), carrier sense multiple access/collision detection (CSMA/CD) bus architecture (IEEE 802.3, basically the Ethernet architecture) and token bus architecture (IEEE 802.4, the recommended LAN architecture for the manufacturing atomation protocol, MAP). Each of these architectures is assumed to be implemented using electrical conductors; newer architectures using fibre optics (such as FDDI) are currently being studied. The primary reliability parameter studied is average source-destination availability. The models are based on information in the standards plus implementation details, using more implementation details than previous reliability models. Approximate analyses, which reflect all architecture details that appear to be pertinent to availability, have been developed, rather than exact analyses which ignore fine details. One conclusion is that details neglected in previous models have major effects on, and may be the most important factors determining, source–destination availability. At present, no measured values for the relevant parameters are obtainable, however, so all of our computations are based on arbitrary ‘guesstimates’ of these parameter values. A few other conclusions can be reached. Since major components of the bus networks (CSMA/CD and token bus) are similar, reliabilities of these networks are also similar, with differences determined primarily by differences in parameters. Adequate data to describe these differences were not obtainable, so our example computations for the two bus networks yield essentially the same results. Although its use of an active communications medium, instead of the passive bus used by the other architectures, may decrease reliability of the token ring, the token ring architecture gives more flexibility in bypassing or recovering from error situations. In some situations this could make the token ring the most reliable LAN, but ‘reasonable’ choices of parameter values could make any of the LANs most reliable. If many stations are inactive, however, any reliability advantage for token rings would be eliminated by even a small probability that inactive stations are not successfully bypassed     

Application of genetic algorithm for reliability allocation in nuclear power plants

Reliability allocation is an optimization process of minimizing the total plant costs subject to the overall plant safety goal constraints. Reliability allocation was applied to determine the reliability characteristics of reactor systems, subsystems, major components and plant procedures that are consistent with a set of top-level performance goals; the core melt frequency, acute fatalities and latent fatalities. Reliability allocation can be performed to improve the design, operation and safety of new and/or existing nuclear power plants. Reliability allocation is a kind of a difficult multi-objective optimization problem as well as a global optimization problem. The genetic algorithm, known as one of the most powerful tools for most optimization problems, is applied to the reliability allocation problem of a typical pressurized water reactor in this article. One of the main problems of reliability allocation is defining realistic objective functions. Hence, in order to optimize the reliability of the system, the cost for improving and/or degrading the reliability of the system should be included in the reliability allocation process. We used techniques derived from the value impact analysis to define the realistic objective function in this article.     

Quantized hopfield networks for reliability optimization

The use of neural networks in the reliability optimization field is rare. This paper presents an application of a recent kind of neural networks in a reliability optimization problem for a series system with multiple-choice constraints incorporated at each subsystem, to maximize the system reliability subject to the system budget. The problem is formulated as a nonlinear binary integer programming problem and characterized as an NP-hard problem. Our design of neural network to solve efficiently this problem is based on a quantized Hopfield network. This network allows us to obtain optimal design solutions very frequently and much more quickly than others Hopfield networks.     

Two-terminal reliability analyses for a mobile ad hoc wireless network

Reliability is one of the most important performance measures for emerging technologies. For these systems, shortcomings are often overlooked in early releases as the cutting edge technology overshadows a fragile design. Currently, the proliferation of the mobile ad hoc wireless networks (MAWN) is moving from cutting edge to commodity and thus, reliable performance will be expected. Generally, ad hoc networking is applied for the flexibility and mobility it provides. As a result, military and first responders employ this network scheme and the reliability of the network becomes paramount. To ensure reliability is achieved, one must first be able to analyze and calculate the reliability of the MAWN. This work describes the unique attributes of the MAWN and how the classical analysis of network reliability, where the network configuration is known a priori, can be adjusted to model and analyze this type of network. The methods developed acknowledge the dynamic and scalable nature of the MAWN along with its absence of infrastructure. Thus, the methods rely on a modeling approach that considers the probabilistic formation of different network configurations in a MAWN. Hence, this paper proposes reliability analysis methods that consider the effect of node mobility and the continuous changes in the network's connectivity.     

A new algorithm in enumerating all minimal paths in a sparse network

In this paper an efficient algorithm is proposed that generates all minimal paths in a sparse network. When we analyze a complex network reliability, it is important to enumerate all minimal paths. The DFS algorithm is the well-known method for enumerating all minimal paths. Shen has provided a DFS algorithm that is simple and easy to program. Our proposed algorithm is composed of Shen's algorithm and some additional processes. Computational results show that our algorithm is more efficient than Shen's for many sparse networks.     

A discrete-time Bayesian network reliability modeling and analysis framework

Dependability tools are becoming an indispensable tool for modeling and analyzing (critical) systems. However the growing complexity of such systems calls for increasing sophistication of these tools. Dependability tools need to not only capture the complex dynamic behavior of the system components, but they must be also easy to use, intuitive, and computationally efficient. In general, current tools have a number of shortcomings including lack of modeling power, incapacity to efficiently handle general component failure distributions, and ineffectiveness in solving large models that exhibit complex dependencies between their components. We propose a novel reliability modeling and analysis framework based on the Bayesian network (BN) formalism. The overall approach is to investigate timed Bayesian networks and to find a suitable reliability framework for dynamic systems. We have applied our methodology to two example systems and preliminary results are promising. We have defined a discrete-time BN reliability formalism and demonstrated its capabilities from a modeling and analysis point of view. This research shows that a BN based reliability formalism is a powerful potential solution to modeling and analyzing various kinds of system components behaviors and interactions. Moreover, being based on the BN formalism, the framework is easy to use and intuitive for non-experts, and provides a basis for more advanced and useful analyses such as system diagnosis.     

An Efficient Reliability Evaluation Approach for Networks with Simultaneous Multiple‐Node‐Pair Flow Requirements

This paper proposes an efficient approach for reliability evaluation of multiple‐sources and multiple‐destinations flow networks. The proposed approach evaluates multiple node pair capacity related reliability. The proposed approach is a three‐step approach; in the first step, it enumerates network minimal cut sets. These network minimal cut sets are then used to enumerate subset cuts in the second step. Third step involves the evaluation of multiple node pair capacity related reliability from the enumerated subset cuts using a multi‐variable inversion sum‐of‐disjoint set approach. The proposed approach can be used for optimal network design as it combines multiple performance requirements, that is, flow requirements between multiple node pairs and network reliability, in a single criterion. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved algorithm for searching all minimal cuts in modified networks

A modified network is an updated network after inserting a branch string (a special path) between two nodes in the original network. Modifications are common for network expansion or reinforcement evaluation and planning. The problem of searching all minimal cuts (MCs) in a modified network is discussed and solved in this study. The existing best-known methods for solving this problem either needed extensive comparison and verification or failed to solve some special but important cases. Therefore, a more efficient, intuitive and generalized method for searching all MCs without an extensive research procedure is proposed. In this study, we first develop an intuitive algorithm based upon the reformation of all MCs in the original network to search for all MCs in a modified network. Next, the correctness of the proposed algorithm will be analyzed and proven. The computational complexity of the proposed algorithm is analyzed and compared with the existing best-known methods. Finally, two examples illustrate how all MCs are generated in a modified network using the information of all of the MCs in the corresponding original network.     

A path-based algorithm for evaluating the k-out-of-n flow network reliability

Evaluating the network reliability is an important topic in the planning, designing and control of systems. The minimal path (MP, an edge set) set is one of the major, fundamental tools for evaluating network reliability. A k-out-of-n MP is a union of some MPs in a k-out-of-n flow network in which some nodes must receive flows from their k input distinctive edges (each input edge has one flow) to generate one flow, where k is an integer number between 2 and n. In this study, a very simple a-lgorithm based on some intuitive theorems that characterize the k-out-of-n MP structure and the relationship between k-out-of-n MPs and k-out-of-n MP candidates is developed to solve the k-out-of-n flow network reliability by finding the k-out-of-n MPs between two special nodes. The proposed algorithm is easier to understand and implement. The correctness of the proposed algorithm will be analyzed and proven. One example is illustrated to show how all k-out-of-n MPs are generated and verified in a k-out-of-n flow network using the proposed algorithm. The reliability of one example is then computing using the same example.