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.     

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.     

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.     

A Parallel Strategy for the Logical‐probabilistic Calculus‐based Method to Calculate Two‐terminal Reliability

The theory of network reliability has been applied to many complicated network structures, such as computer and communication networks, piping systems, electricity networks, and traffic networks. The theory is used to evaluate the operational performance of networks that can be modeled by probabilistic graphs. Although evaluating network reliability is an Non‐deterministic Polynomial‐time hard problem, numerous solutions have been proposed. However, most of them are based on sequential computing, which under‐utilizes the benefits of multi‐core processor architectures. This paper addresses this limitation by proposing an efficient strategy for calculating the two‐terminal (terminal‐pair) reliability of a binary‐state network that uses parallel computing. Existing methods are analyzed. Then, an efficient method for calculating terminal‐pair reliability based on logical‐probabilistic calculus is proposed. Finally, a parallel version of the proposed algorithm is developed. This is the first study to implement an algorithm for estimating terminal‐pair reliability in parallel on multi‐core processor architectures. The experimental results show that the proposed algorithm and its parallel version outperform an existing sequential algorithm in terms of execution time. Copyright © 2015 John Wiley & Sons, Ltd.     

Nano-carrier mediated co-delivery of methyl prednisolone and minocycline for improved post-traumatic spinal cord injury conditions in rats

Objective: The objective of this study is to investigate the fate of albumin coupled nanoparticulate system over non-targeted drug carrier in the treatment of hemisectioned spinal cord injury (SCI).

Significance: Targeted delivery of methyl prednisolone (MP) and minocycline (MC) portrayed improved therapeutic efficacy as compared with non-targeted nanoparticles (NPS).

Methods: Albumin coupled, chitosan stabilized, and cationic NPS (albumin-MP?+?MC???NPS) of poly-(lactide-co-glycolic acid) were prepared using the emulsion solvent evaporation method. Prepared NPS were characterized for drug entrapment efficiency, particle size, poly-dispersity index (PDI), zeta potential, and morphological characteristics. Their evaluation was done based on the pharmaceutical, toxicological, and pharmacological parameters.

Results and discussion: In vitro release of MP?+?MC from albumin-MP?+?MC???NPS and MP?+?MC???NPS was observed to be very controlled for the period of eight days. Cell viability study portrayed non-toxic nature of the developed NPS. Albumin-MP?+?MC???NPS showed prominent anti-inflammatory potential as compared with non-targeted NPS (MP?+?MC???NPS) when studied in LPS-induced inflamed astrocytes. Albumin-MP?+?MC???NPS reduced lesional volume and improved behavioral outcomes significantly in rats with SCI (hemisectioned injury model) when compared with that of MP?+?MC???NPS.

Conclusions: Albumin-coupled NPS carrier offered an effective method of SCI treatment following safe co-administration of MP and MC. The in vitro and in vivo effectiveness of MP?+?MC was improved tremendously when compared with the effectiveness showed by MP?+?MC???NPS. That could be attributed to the site specific, controlled release of MP?+?MC to the inflammatory site.     

An efficient method for reliability evaluation of multistate networks given all minimal path vectors

The multistate networks under consideration consist of a source node, a sink node, and some independent failure-prone components in between the nodes. The components can work at different levels of capacity. For such a network, we are interested in evaluating the probability that the flow from the source node to the sink node is equal to or greater than a demanded flow of d units. A general method for reliability evaluation of such multistate networks is using minimal path (cut) vectors. A minimal path vector to system state d is called a d-MP. Approaches for generating all d-MPs have been reported. Given that all d-MPs have been found, the issue becomes how to evaluate the probability of the union of the events that the component state vector is greater than or equal to at least one of the d-MPs. There is a need for a more efficient method of determining the probability of this union of events. In this paper, we report an efficient recursive algorithm for this union probability evaluation based on the Sum of Disjoint Products (SDP) principle, and name it the Recursive Sum of Disjoint Products (RSDP) algorithm. The basic idea is that, based on the SDP principle and a specially defined “maximum” operator, “⊕”, the probability of a union with L vectors can be calculated via calculating the probabilities of several unions with L-1 vectors or less. The correctness of RSDP is illustrated. The efficiency of this algorithm is investigated by comparing it with an existing algorithm that is generally accepted to be efficient. It is found that RSDP is more efficient than the existing algorithm when the number of components of a system is not too small. RSDP provides us with an efficient, systematic and simple approach for evaluating multistate network reliability given all d-MPs.     

Cutset enumeration of network systems with link and node failures

Network reliability analysis has received considerable attention and is thus widely studied to predict and prevent any network failure. However, most of such works presume perfectly reliable nodes. Although a few studies have considered both link and node failures, none of these methods has utilized the minimal paths or cuts, which are considered as fundamental approaches in the network reliability evaluation. An efficient method for deducing the minimal cutsets of a system subject to both link and node failures from the minimal cutsets of the system, which assumes perfect node reliability, is presented. The proposed method does not require re-enumeration of minimal cutsets for the additional consideration of the node failures. For a simple extension of such a method, the proposed approach can be embedded in any exact or approximate algorithm to account for link failures as well as node failures. As a result, the application of this method would be more realistic and valuable in practice for the reliability evaluation of networks with unreliable nodes.     

A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability

The weighted multicommodity multistate unreliable network (WMMUN) is a novel network composed of multistate unreliable components (arcs and nodes) capable of transmitting different types of commodities in which capacity weight varies with components. It is an extension of the multistate network. The current method for evaluating the directed WMMUN reliability has been derived from minimal cut (MC) based algorithm. The existing best-known method needed extensive comparison and verification, and failed to find the real directed WMMUN reliability. A very simple algorithm based on minimal paths (MPs) is developed for the WMMUN reliability problem. The correctness and computational complexity of the proposed algorithm will be analyzed and proven. An example is given to illustrate how the WMMUN reliability is evaluated using the proposed algorithm. The relationships among all different versions of MPs are also clarified.     

Element substitution algorithm for general two-terminal network reliability analyses

The computation of the reliability of two-terminal networks is a classical reliability problem. For these types of problems, one is interested, from a general perspective, in obtaining the probability that two specific nodes can communicate. This paper presents a holistic algorithm for the analysis of general networks that follow a two-terminal rationale. The algorithm is based on a set replacement approach and an element inheritance strategy that effectively obtains the minimal cut sets associated with a given network. The vast majority of methods available for obtaining two-terminal reliability are generally based on assumptions about the performance of the network. Some methods assume network components can be in one of two states: (i) either completely failed; or (ii) perfectly functioning, others usually assume that nodes are perfectly reliable and thus, these methods have to be complemented or transformed to account for node failure, and the remaining methods assume minimal cut sets can be readily computed in order to analyze more complex network and component behavior. The algorithm presented in this paper significantly differs from previous approaches available in the literature in the sense that it is based on a predecessor matrix and an element substitution technique that allows for the exact computation of minimal cut sets and the immediate inclusion of node failure without any changes to the pseudo-code. Several case networks are used to validate and illustrate the algorithms.     

System reliability for joint minimal paths under time constraint

The quickest path in a transmission problem for a multistate flow network is considered in this article. In this problem, a given amount of data is transmitted to the destination through multiple minimal paths (MPs) simultaneously, and the probability of complete transmission within a time constraint is of interest. In particular, the MPs are joint such that a constriction occurs. An algorithm is developed by applying Monte Carlo simulation to find the system reliability. Furthermore, the proposed algorithm can be used to manage situations with either joint or disjoint MPs. Although the system reliability obtained from this algorithm is an approximate value, the experiments and inference statistics indicate that the expected value is very close to the actual system reliability.     

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.     

Reliability assessment of restructured power systems using optimal load shedding technique

Power systemrestructuring and deregulation has changed the strategy of reliabilitymanagement of a power system. Load shedding, and generation and reserve re-dispatch methods used in the existing reliability evaluation techniques have to be improved to incorporate these changes. An optimisation technique, incorporating those changes, is proposed in this study to determine load curtailment and generation re-dispatch for each contingency state in the reliability evaluation of restructured power systems with the Poolco market structure. The problem is formulated using the optimal power flow (OPF) technique. The objective of the problem is to minimise the total system cost, which includes generation, reserve and interruption costs, subject to market and network constraints. A model for the contingency management of a Poolco power market is presented to include generation and reserve biddings, reliability considerations and transmission network constraints in reliability evaluation. Both supply side reliability for a generation company (Genco) and demand-side reliability for a customer can be calculated using the technique. The proposed technique can be used to evaluate both conventional and restructured power systems, and can provide both economic and reliability information for the independent system operator to manage system reliability, for Gencos to enhance their reliability, and for customer to select suppliers. The modified IEEE-RTS with the Poolco market has been analysed to illustrate the techniques. The results obtained using the proposed technique have been compared with those from the existing load shedding techniques.     

A simple algorithm for evaluating the k-out-of-n network reliability

Evaluating the network reliability is an important topic in the planning, designing, and control of systems. The minimal cut set (MC, an edge set) is one of the major and fundamental tools for evaluating network reliability. A k-out-of-n MC is a special MC in a k-out-of-n network in which some nodes must receive at least k flows from their n input edges, where k is an integer number between 1 and n. In this study, an alternative method is given first to define a MC using a node set (called MCN) in k-out-of-n networks. A very simple algorithm based on some intuitive theorems that characterize the structure of the MCN and the relationship between MC and MCN is developed to solve the k-out-of-n network reliability by finding the k-out-of-n MCs between two special nodes. The proposed algorithm is not only easier to understand and implement, but is also better than the existing algorithm. The correctness of the proposed algorithm will be analyzed and proven. Two examples are illustrated to show how all k-out-of-n MCs are generated and verified in a k-out-of-n network using the proposed algorithm. The reliability of one example is then computing using one example.     

Reliability analysis of shuffle-exchange network systems

Shuffle-exchange networks (SENs) have been widely considered as practical interconnection systems due to their size of its switching elements (SEs) and uncomplicated configuration. SEN is a network among a large class of topologically equivalent multistage interconnection networks (MINs) that includes omega, indirect binary n-cube, baseline, and generalized cube. In this paper, SEN with additional stages that provide more redundant paths are analyzed. A common network topology with a 2×2 basic building block in a SEN and its variants in terms of extra-stages is investigated. As an illustration, three types of SENs are compared: SEN, SEN with an additional stage (SEN+), and SEN with two additional stages (SEN+2). Finally, three measures of reliability: terminal, broadcast, and network reliability for the three SEN systems are analyzed.     

Building confidence in the reliability assessment of thermal-hydraulic passive systems

Thermal-hydraulic (T-H) passive systems play a crucial role in the development of future solutions for nuclear power plant technologies. A fundamental issue still to be resolved is the quantification of the reliability of such systems.The difficulty comes from the uncertainties in the evaluation of their performance, because of the lack of experimental and operational data and of validated models of the phenomena involved. The uncertainties concern the deviations of the underlying physical principles from the expected T-H behaviour, due to the onset of physical phenomena infringing the system performance or to changes in the initial/boundary conditions of system operation.In this work, some insights resulting from a survey on the technical issues associated with estimating the reliability of T-H passive systems in the context of nuclear safety are first provided. It is concluded that the most realistic assessment of the passive system response to the uncertain accident conditions can be achieved by Monte-Carlo (MC) sampling of the system uncertain parameters followed by the simulation of the accident evolution by a detailed mechanistic T-H code. This procedure, however, requires considerable and often prohibitive computational efforts for achieving acceptable accuracies, so that a limitation on the MC sample size, i.e. on the number of code runs, is necessarily forced onto the analysis. As a consequence, it becomes mandatory to provide quantitative measures of the uncertainty of the computed estimates.To this aim, two classes of statistical methods are proposed in the paper to quantify, in terms of confidence intervals, the uncertainties associated with the reliability estimates. The first method is based on the probability laws of the binomial distribution governing the stochastic process of system success or failure. The second method is founded on the concept of bootstrapping, suitable to assess the accuracy of estimators when no prior information on their distributions is available. To the authors’ knowledge, it is the first time that these methods are applied to quantitatively bracket the confidence on the estimates of the reliability of passive systems by MC simulation.The two methods are demonstrated by an application to a real passive system of literature.     

Development and Application of Multiple‐Probe Scanning Probe Microscopes

In the research of advanced materials based on nanoscience and nanotechnology, it is often desirable to measure nanoscale local electrical conductivity at a designated position of a given sample. For this purpose, multiple‐probe scanning probe microscopes (MP‐SPMs), in which two, three or four scanning tunneling microscope (STM) or atomic force microscope (AFM) probes are operated independently, have been developed. Each probe in an MP‐SPM is used not only for observing high‐resolution STM or AFM images but also for forming an electrical contact enabling nanoscale local electrical conductivity measurement. The world's first double‐probe STM (DP‐STM) developed by the authors, which was subsequently modified to a triple‐probe STM (TP‐STM), has been used to measure the conductivities of one‐dimensional metal nanowires and carbon nanotubes and also two‐dimensional molecular films. A quadruple‐probe STM (QP‐STM) has also been developed and used to measure the conductivity of two‐dimensional molecular films without the ambiguity of contact resistance between the probe and sample. Moreover, a quadruple‐probe AFM (QP‐AFM) with four conductive tuning‐fork‐type self‐detection force sensing probes has been developed to measure the conductivity of a nanostructure on an insulating substrate. A general‐purpose computer software to control four probes at the same time has also been developed and used in the operation of the QP‐AFM. These developments and applications of MP‐SPMs are reviewed in this paper.     

Fast approximate methods for the reliability analysis of computer networks

The complexity of computer communication networks has taken a dramatic upswing, following significant developments in electronic technology such as medium and large scale integrated circuits and microprocessors. Although components of a computer communication network are broadly classified into software, hardware and communications, the most important problem is that of ensuring the reliable flow of information from source to destination. An important parameter in the analysis of these networks is to find the probability of obtaining a situation in which each node in the network communicates with all other remaining communication centres (nodes). This probability, termed as overall reliability, can be determined using the concept of spanning trees. As the exact reliability evaluation becomes unmanageable even for a reasonable sized system, we present an approximate technique using clustering methods. It has been shown that when component reliability ⩾ 0.9, the suggested technique gives results quite close to those obtained by exact methods with an enormous saving in computation time and memory usage. For still quicker reliability analysis while designing the topological configuration of real-time computer systems, an empirical form of the reliability index is proposed which serves as a fairly good indicator of overall reliability and can be easily incorporated in a design procedure, such as local search, to design maximally reliable computer communication network.     

Optimal reserve management for restructured power generating systems

This paper presents a technique to determine the optimal reserve structure (reserve providers and the corresponding reserve capacity) for a restructured power generating system (GS). The reserve of a GS can be provided by its own generating units and can also be purchased from other GSs through the reserve agreements. The objective of reserve management for a GS is to minimize its total reserve cost while satisfying the reliability requirement. The reserve management is a complex optimization problem, which requires a large amount of calculations. In order to simplify the evaluation, a complex generating system (CGS) consisting of different GSs and the corresponding transmitting network is represented by its multi-state reliability equivalents. The universal generating functions (UGFs) of these equivalents are developed and the special operators for these UGFs are defined to evaluate the reliability of a particular GS, which has reserve agreements with other GSs in the CGS. The genetic algorithm (GA) has been used to solve the optimization problem. An improved power system-IEEE reliability test system is used to illustrate the technique.     

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.     

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．