Structure Functions and Minimal Path Sets

In order to take advantage of the computer in the numerical calculation, in view of the fault tree qualitative analysis, a new method of fault tree analysis, numerical methods, was proposed on the basis of absorbing merits of the prime number method and determinant method. The fault tree's minimum cut sets and path sets can be calculated effectively with this method. Consequently, a specific example about calculation of the minimum cut sets was demonstrated with Scilab in this paper.

This article will include three important methods for extracting minimal path sets from a complex network, and a comparison will be made between these methods to choose the best one for accessing minimal path sets. Also, this article will discuss HEWEIDY'S METHOD, which is a new and effective method for calculating the importance of each component of a complex network and its levels. This method depends entirely on the relationship between minimal path sets and minimal cut sets, and the latter we will extract from minimal path sets.

The aim was to abate the casualty, wealth loss, and frequency of coal mine accident and to understand the pathogenesis, influencing factor, and the hazard of coal dust explosion, which is one of the major accidents in coal mine. Take Shen Bao surface coal mine for example. Fault tree analysis is used to make the careful analysis of the basic events leading to the accident under the production system and the hazard of the coal mine production system. On the basis of it, we put forward the classification of the coal dust explosion hazard and construct mathematical functions, and calculating the occurring probability of the top event and coal dust explosion data of minimum cut sets, minimum path sets. After all the analyses, the results show that the more the basic events, the lower the probability of their simultaneous occurrence in minimum cut sets, which means the lower possibility of coal mine accident. Also we give the safety recommendations on the basis of conclusion that the hazard is mainly on coal mine gas explosion, spontaneous combustion of coal, and high concentration of oxygen.

Bounds for coherent reliability structures

This thesis adopts security system engineering methods to analyze the public security incidents of serious water pollution in Three Gorges Reservoir and draw a diagram of fault tree analysis which directly indicates every possible basic event and its logical relations leading to top incident.Through qualitative analysis of Fault Tree Analysis,the minimal cut sets,the minimal path sets and the order of the structure importance have been found,which demonstrates the possible ways of protecting public security incidents of serious water pollution.

Sand casting operations, though commonplace, pose a significant threat of explosion accidents. This paper presents a novel sand casting safety assessment technique based on fault tree analysis, Heinrich accident triangle, hazard and operability–layer of protection analysis (HAZOP–LOPA) and bow tie model components. Minimal cut sets and minimal path sets are first determined based on fault tree analysis, then the frequency of sand casting explosion accidents is calculated based on the Heinrich accident triangle. Third, the risk level of venting quality can be reduced by adopting HAZOP–LOPA; the residual risk level of venting quality remains excessive even after adopting two independent protective layers. The bow tie model is then adopted to determine the causes and consequences of venting quality. Five preventative measures are imposed to enhance the venting quality of foundry sand accompanied by 16 mitigative safety measures. Our results indicate that the risk attributable to low foundry sand venting quality can be minimized via bow tie analysis.

Summary form only given. Tubular and tree structures appear very commonly in biomedical images like vessels, microtubules or neuron cells. Minimal paths have been used for long as an interactive tool to segment these structures as cost minimizing curves. The user usually provides start and end points on the image and gets the minimal path as output. These minimal paths correspond to minimal geodesics according to some adapted metric. They are a way to find a (set of) curve(s) globally minimizing the geodesic active contours energy. Finding a geodesic distance can be solved by the Eikonal equation using the fast and efficient Fast Marching method. In the past years we have introduced different extensions of these minimal paths that improve either the interactive aspects or the results. For example, the metric can take into account both scale and orientation of the path. This leads to solving an anisotropic minimal path in a 2D or 3D+radius space. On a different level, the user interaction can be minimized by adding iteratively what we called the keypoints, for example to obtain a closed curve from a single initial point. The result is then a set of minimal paths between pairs of keypoints. This can also be applied to branching structures in both 2D and 3D images. We also proposed different criteria to obtain automatically a set of end points of a tree structure by giving only one starting point. More recently, we introduced a new general idea that we called Geodesic Voting or Geodesic Density. The approach consists in computing geodesics between a given source point and a set of points scattered in the image. The geodesic density is defined at each pixel of the image as the number of geodesics that pass over this pixel. The target structure corresponds to image points with a high geodesic density. We will illustrate different possible applications of this approach. The work we will present involved as well F. Benmansour, Y. Rouchdy and J. Mille at CEREMADE.

Computing system reliability is a classical engineering reliability problem and was modeled using different computational approaches for many years. For systems which include a large number of components, one modeling approach is to consider the system components as vertices of a network graph, with the integrated components connected by edges. Wireless sensor networks follow very close this network graph model, with the access medium used for communication between the sensor nodes modeled as edges and the sensor nodes modeled as vertices. Probability and reliability theory consider the minimal path set as the lowest number of components whose functioning assures the operation of the system. This work models the reliability of wireless sensor networks using minimal path sets defined as the minimal set of functioning sensor networks that ensures a certain threshold of events detected by the sensor network.

Minimal pathset and minimal cutsets using search technique

This paper proposes an efficient approach to enumerate the subsets of cutsets group (SCG) of a communication network having heterogeneous link capacities to evaluate capacity related reliability (CRR) using minimal cutsets. The efficient methodologies in vogue use a priori information of either minimal pathsets or cutsets of the network, which can block or allow a required amount of flow through the network, termed as a first step in CRR evaluation. In the second step, the disjoint sets of the qualified cutsets or pathsets are obtained using an appropriate sum of disjoint product (SDP) approach. Efficient approaches do exist for the second step to obtain the mutually disjoint terms. In this paper, CRR evaluation uses minimal cutsets and an efficient technique to enumerate irredundant SCG. A comparison with respect to the number of subsets of cutsets generation, number of external/internal redundant subsets removal in obtaining irredundant SCG with recent algorithms have been made to show less computational efforts in using the proposed approach and thus a better performance than the existing approaches.

In this article we introduce generalizations of several well-known reliability bounds. These bounds are based on arbitrary partitions of the family of minimal path or cut sets of the system and can be used for approximating the reliability of any coherent structure with i.i.d. components. An illustration is also given of how the general results can be applied for a specific reliability structure (two-dimensional consecutive-k1 x k2-out-of-n1x n2 system) along with extensive numerical calculations revealing that, in most cases, the generalized bounds perform better than other available bounds in the literature for this system.

To solve the problems on quick achieving reliability and the minimal path sets (MPS) of a system with GO Methodology, a Binary Decision Diagram (BDD) based new GO methodology algorithm is introduced. This technique can avoid the shared signals and combination explosion problems simultaneously. Detailed steps with a case study are presented to explain the analysis procedure of this technique, firstly, establish the GO model and transform it into a directed acyclic diagram (DAG), logic tree and BDD successively; then minimize the BDD according to the Without Rule; at last, this system reliability and MPS can be achieved. The results of the studied case verify the validity and effectiveness of this algorithm.

A fixed minimal path array method of evaluating reliability indices of power systems

A heuristic minimal path sets method for analyzing seismic reliability of lifeline networks is proposed. For large-scale lifeline networks reliability computation can become prohibitive or inaccurate using the current enumeration methods. Although a few studies have considered both node and link failures, none of these methods has utilized the minimal paths method. This paper proposes a minimal path algorithm to evaluate reliability of relatively large lifeline networks with unreliable nodes and links. As the primary task, the method can deduce all minimal paths of a directed/undirected network. In the algorithm, minimal paths for both nodes and links are traced performing several procedures. The terminal-pair reliability of the network is then evaluated by performing an efficient Monte Carlo simulation as an alternative to exact reliability calculation methods. In terms of computational speed, the results obtained compare well with existing algorithms. The algorithm requires minimum memory storage and minimum user-defined data to represent the topology of a network. A series of case studies illustrate that the method can be used to evaluate reliability of the large-scale lifeline systems subject to node and link failures, efficiently.

Reliability assessment techniques and programs handling is an important issue for both power systems planning and testing in existing power system configurations. The Assessment techniques are suitable for detecting weak points in the reliability assessment. The reliability study of bulk power systems indicates the ability of the composite generation and transmission system to satisfy the load demand at major load points. The major burden of the developed methods used is the computation time required to solve a large number of credible contingencies or outage states. This paper presents a novel approach capable of the reliability evaluation for real large-size networks using normal size computers. It calculates the reliability indices at individual load buses and reliability of the whole system. The effect of the loading factor between loads on reliability is also investigated. The proposed approach is expanded to calculate the reliability of composite generation and transmission system taking the following constraints into consideration: amount of reliability of system generation, amount of reliability of transmission lines, maximum system generation capacity, maximum transmission lines capacity and maximum connected load at each bus. The approach is based on the minimal path set and dual fault tree techniques. A new concept of constant reliability region, which is utilized in the field of optimum operation of power networks, is introduced. A special program is developed for the proposed technique. The comparison between the proposed and the previous techniques confirms that the proposed method is more accurate and precise.