Generalized reliability bounds for coherent structures

In this short note we give and discuss a general multilinear expression of the structure function of an arbitrary semicoherent system in terms of its minimal path and cut sets. We also examine the link between the number of minimal path and cut sets consisting of 1 or 2 components and the concept of structure signature of the system.

Bounds for coherent reliability structures

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.

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.

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.

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.

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 subject of research is to determine the functional safety indicators of a fault-tolerant safety-critical system, namely, the minimal cut sets’ probability for a given duration of the system’s operation, using the state transition diagram (STD). The aim is to create a new method for analyzing the functional safety of a fault-tolerant safety-critical system. This method is based on the methodology of developing models of operational reliability behavior in the form of STD. This methodology provides a detailed representation of inoperable states and their relation with pre-failure (inoperable critical) states. The task is to propose a new classification for inoperable states of the STD to obtain all possible emergencies in the same space of inoperable states. This approach allows consideration the correlations between the failures, that it is impossible to use the fault trees. Since the space of inoperable states can reach hundreds and thousands of states, a method is proposed for their automated determination according to the classification. The state space method was used to conduct the validation of the method of functional safety analysis. The following results were obtained: the system of Chapman-Kolmogorov differential equations is formed in accordance with the STD and it provides the dependence of the functional safety indicator – the minimal cut sets’ probability as a function of the operational duration of the fault-tolerant safety-critical system. This dependence is called the emergency function. The method for determining the emergency function is based on the usage of the emergency mask. Note that the proposed model of operational reliability behavior in the form of STD provides the possibility to conduct both the functional safety and the reliability indicators. The value of the minimal cut sets’ probability for a given duration of operation is determined using the fault tree for the validation of the proposed method of functional safety analysis. The fault tree was built by Reliasoft BlockSim software. The obtained value coincides with the value of the minimal cut sets’ probability, which was defined by the emergency function for the same operational duration. Thus, the designer can comprehensively analyze the feasibility of introducing redundancy (structural, temporal, functional). Conclusions: the scientific novelty of the obtained results is the following: the new method for determining safe, critical and catastrophic states in the set of inoperable states is used in the methodology of the STD developing to obtain the stochastic model of operational reliability behavior of fault-tolerant safety-critical system. This technique ensures an automated defining of emergency function by using an improved structural-automatic model.

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

Fussell-Vesely Importance (FVI) is one of the most commonly used importance measures. It is based on the concept of Minimal Cut Sets (MCSs), and it quantifies the contribution of a system component to system failure. In paper (Kvassay et al. 2015), the algorithm for identification of all system MCSs based on Direct Partial Logic Derivatives (DPLDs) has been considered. These MCSs are then used to compute the FVI. However, the FVI of a system component depends only on MCSs that contain the considered component, i.e. it is not necessary to identify all MCSs of the system. This implies that it is useful to develop algorithms that will identify not all system MCSs but only those in which a specific component occurs. Such algorithms can be used to compute the FVI without a priori knowledge of MCSs. In this paper, a new algorithm for this task is proposed. The algorithm is based on a relation between DPLDs and MCSs that is also considered in this paper. of algorithms for identification or generation of MCSs of investigated system. These algorithms are developed mainly on the basis of applied fault trees (Sinnamon & Andrews 1997, Vatn 1992) or networks (Emadi & Afrakhte 2014, Rebaiaia & Ait-Kadi 2013). Another algorithm for identification of system MCSs has been considered in paper (Kvassay et al. 2015). This algorithm is based on tools of logical differential calculus, and it can be used for systems of any type (not only for systems presented as networks or for systems described by fault trees). Logical differential calculus has been developed for analysis of dynamic properties of logic functions. Direct Partial Logic Derivatives (DPLDs) are essential part of this tool (Tapia et al. 1991). Their use in reliability analysis has been considered in several papers (Zaitseva 2003, Zaitseva 2012, Zaitseva et al. 2015). These papers have showed that DPLDs are very appropriate for identification of situations in which failure/repair of a system component results in system failure/repair. This fact has been used to develop algorithms for defining system boundary states and for calculation of some measures that can be used to evaluate system reliability. In this paper, we develop ideas presented in paper (Kvassay et al. 2015) to propose an algorithm that identifies not all system MCSs but only MCSs in which a specified component is presented. Such MCSs are useful in computation of FVI of the considered component. As a result new method for calculation of this IM is developed. This method is

Minimal pathset and minimal cutsets using search technique

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.

Elementary modes (EMs) and minimal cut sets (MCSs) provide important techniques for metabolic network modeling. Whereas EMs describe minimal subnetworks that can function in steady state, MCSs are sets of reactions whose removal will disable certain network functions. Effective algorithms were developed for EM computation while calculation of MCSs is typically addressed by indirect methods requiring the computation of EMs as initial step. In this contribution, we provide a method that determines MCSs directly without calculating the EMs. We introduce a duality framework for metabolic networks where the enumeration of MCSs in the original network is reduced to identifying the EMs in a dual network. As a further extension, we propose a generalization of MCSs in metabolic networks by allowing the combination of inhomogeneous constraints on reaction rates. This framework provides a promising tool to open the concept of EMs and MCSs to a wider class of applications. utz-uwe.haus@math.ethz.ch; klamt@mpi-magdeburg.mpg.de Supplementary data are available at Bioinformatics online.

Since their introduction in form of a canonical representation of logical functions, the Binary Decision Diagrams (BDDs) gained a wide acceptance in numerous industrial applications. This paper summarizes the properties of BDD representation of Minimal Cut Sets (MCS) of Fault Tree (FT) models most typically encountered in nuclear energetics. Cut sets from MCS are defined as paths from the top BDD node to terminal nodes in the BDD, on which a quantitative and qualitative FT analysis (FTA) is performed. The core of the FTA on the BDDs is performed with help of two fundamental algorithms, one for conditional probability evaluation and another for the selection of cut sets. The accuracy of conditional probability evaluation represents an essential feature for an unbiased quantitative analysis, such as the top event probability or the determination of event importance measures. The cut set selection algorithm is shown in a generic version introducing logical predicates for its selection criteria. As it is known, the efficiency of depicted algorithms depends only on the number of BDD nodes used for the FT representation. In order to appraise the compactness of the BDD representation of FT models, their characteristics have herein been evaluated on several real-life models from the Nuclear Power Plant Krško. The extraordinariness of the compactness of the BDD representation reflects in its ability to implement advanced dynamic analysis (i.e. what-if) of FT models. The efficiency of such an approach is recognized by commercial vendors upgrading their FT Tools to new versions by implementing BDD based algorithms.