Minimal Cut Sets Research Articles

Reliability Modeling and Analysis of Reactor Protection System Based on FPGA

In order to establish a reactor protection system reliability model based on the field programmable gate array (FPGA) to provide effective analysis and verification methods for system safety, this study adopts the fault tree and stochastic Petri net (SPN) models to perform reliability modeling and analysis for the single channel of CANDU reactor shutdown system 1 (SDS1). The analysis by fault tree model provides the minimal cut set. With the top event probability taken as the system fault probability, and in consideration of the fault detection, maintenance and periodic testing, the probability of rejection of the system is obtained by the stochastic Petri net model simulation. The results show that both the fault tree and state space representation are limited to a certain extent, while the stochastic Petri net can reflect the impact of fault detection and periodic tests on the reactor protection system, dynamically present the system reliability, and avoid the problem of state space explosion. Therefore, the stochastic Petri net model established in this study is suitable for the reliability modeling of the reactor protection system.

Applications of FFTA–HFACS for Analyzing Human and Organization Factors in Electric Misoperation Accidents

Human and organizational factors (HOFs) play an important role in electric misoperation accidents (EMAs), but research into the reliability of human factors is still in its infancy in the field of EMAs, and further investment in research is urgently required. To analyze the HOFs in EMAs, a hybrid method including the Human Factors Analysis and Classification System (HFACS) and fuzzy fault tree analysis (FFTA) was applied to EMAs for the first time in the paper. HFACS is used to identify and classify the HOFs with 135 accidents, reorganized as basic events (BEs), intermediate events (IEs), and top event (TE), and develop the architecture of fault tree (FT). Fuzzy aggregation is employed to address experts’ expressions and obtain the failure probabilities of the BEs and the minimal cut sets (MCSs) of the FT. The approach generates BEs failure probabilities without reliance on quantitative historical failure statistics of EMAs via qualitative records processing. The FFTA–HFACS model is applied for quantitative analysis of the probability of failure of electrical mishaps and the interaction between accident risk factors. It can assist professionals in deciding whether and where to take preventive or corrective actions and assist in knowledgeable decision-making around the electric operation and maintenance process. Finally, applying this hybrid method to EMAs, the results show that the probability of an EMAs is 1.0410 × 10−2, which is a risk level that is likely to occur and must be controlled. Two of the most important risk factors are habitual violations and supervisory violation; a combination of risk factors of inadequate work preparation and paralysis, and irresponsibility on the part of employees are also frequent errors.

Optimal allocation of a coherent system with statistical dependent subsystems

AbstractThis paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.

Overheat fault analysis of drillship electric winch drive system

In order to solve the problem of winch motor overheating, this paper analyzes the possible reasons of motor overheating along with the structure and principle of drillship winch. Taking the overheating fault of drillship’s driving motor as the top event, the fault tree model of the overheating problem of the driving motor is established, and the relative weak links of the winch are found out through the minimum cut set. With the result of fault tree analysis as a guide, the lifting device was inspected, the fault reason of the lifting device was found out, and the corresponding solutions were put forward. The results show that the proposed method in the paper can improve the efficiency of fault location.

Derivation of Minimal Cutsets from Minimal Pathsets for a Multi-State System and Utilization of Both Sets in Checking Reliability Expressions

This paper addresses two important useful extensions of binary reliability techniques to multi-state reliability techniques, namely: (a) the problem of complementation or inversion of the function of system success to that of system failure (or equivalently, of deriving the logical minimal cutsets in terms of the logical minimal paths), and (b) the associated problem of hand-checking of a symbolic reliability expression. The paper deals specifically with the reliability of a multi-state delivery network. It presents two complementation procedures, one via the application of multi-state De Morgan’s rules, and the other via the multi-state Boole-Shannon expansion. The paper also illustrates one case in which this complementation is needed, as it outlines a method for checking the reliability of the multi-state system in terms of its logical minimal paths and logical minimal cutsets.

A Multi-Objective Reconfiguration Scheme for Reliability and Energy Usage Enhancement of Distribution Systems in the Presence of Wind Turbines Using the MOHSA Optimization Algorithm

The stochastic nature of the active power generated by wind turbines (WTs) has posed new challenges to the reliability assessment, load flow analysis, and reconfiguration process of distribution systems penetrated with WTs. In this paper, a new optimization approach has been presented to find the best configuration of the distribution system along with optimal locations of WTs. This is aimed at maximizing the reliability of the system, while energy losses are minimized. To this end, based on the graph theory and the system topology, a simple technique is proposed for finding minimal cut sets that could be used for calculating reliability indices. Furthermore, the multiple flow directions created in the presence of WTs cause difficulties in calculating reliability indices and in performing load flow analysis. Accordingly, a new concept called the independent reliability zone is introduced to overcome these problems. In this paper, the multi-objective harmony search algorithm, due to its suitability for multi-objective problems, is employed as a solution for solving the proposed optimization problem. The effect of the proposed approach has been evaluated on both test and real systems. The results show that using the proposed approach, a more practical solution is achieved for low-cost and reliable 24-hour planning of the system in the presence of uncertainties in DGs.

How to incorporate human failure event recovery into minimal cut set generation stage for efficient probabilistic safety assessments of nuclear power plants

Human failure event (HFE) dependency analysis is a part of human reliability analysis (HRA). For efficient HFE dependency analysis, a maximum number of minimal cut sets (MCSs) that have HFE combinations are generated from the fault trees for the probabilistic safety assessment (PSA) of nuclear power plants (NPPs). After collecting potential HFE combinations, dependency levels of subsequent HFEs on the preceding HFEs in each MCS are analyzed and assigned as conditional probabilities. Then, HFE recovery is performed to reflect these conditional probabilities in MCSs by modifying MCSs.Inappropriate HFE dependency analysis and HFE recovery might lead to an inaccurate core damage frequency (CDF). Using the above process, HFE recovery is performed on MCSs that are generated with a non-zero truncation limit, where many MCSs that have HFE combinations are truncated. As a result, the resultant CDF might be underestimated.In this paper, a new method is suggested to incorporate HFE recovery into the MCS generation stage. Compared to the current approach with a separate HFE recovery after MCS generation, this new method can (1) reduce the total time and burden for MCS generation and HFE recovery, (2) prevent the truncation of MCSs that have dependent HFEs, and (3) avoid CDF underestimation. This new method is a simple but very effective means of performing MCS generation and HFE recovery simultaneously and improving CDF accuracy. The effectiveness and strength of the new method are clearly demonstrated and discussed with fault trees and HFE combinations that have joint probabilities.

A Noisy-OR gate based fuzzy fault tree approach for micro-leakage evaluation of bolt-gasket-flange connection (BGFC)

In the natural gas gathering and transportation station, bolt-gasket-flange connection (BGFC) is the main connection mode, but due to its large number, the micro-leakage may result in serious consequences. For this reason, early BGFC micro-leakage evaluation can effectively assist decision-making and prevent the occurrence of accidents. To solve the problem of insufficient field data collection, we proposed a Noisy-OR gate based fuzzy fault tree approach, and calculated the corresponding minimum cut sets and the highest risk factors. Moreover, sensitivity analysis (SA) was used to determine that material problems (wear and corrosion of the sealing surface), man-made operation problems (bolts and flanges) and working conditions (pipe vibration and temperature fluctuations) are the key factors that contributing to the BGFC micro-leakage. In brief, the combination of the fuzzy fault tree analysis and Noisy-OR gate is an effective approach for BGFC micro-leakage evaluation, which is of great significance to the micro-leakage analysis, safe operation, and risk assessment of the gas station.

A quantification methodology of Seismic Probabilistic Safety Assessment for nuclear power plant

A Seismic Probabilistic Safety Assessment (SPSA), unlike other internal or external event analyses, has a very high probability of basic events when a strong earthquake occurs. Because of this high probability, the Core Damage Frequency (CDF) might be overestimated by the Rare Events Approximation (REA) and Minimal Cutset Upper Bound (MCUB) method for general quantitative analysis. To compensate for this overestimation, the exact CDF value can be derived with post-processing software such as an Advanced Cutset Upper Bound Estimator (ACUBE) or Fault Tree Evaluation using Monte Carlo simulation (FTeMC). However, the Minimal Cut Sets (MCSs), which has the same result as the calculated CDF, cannot be derived with both methods. In this paper, we propose a Monte Carlo Simulation Allocation Method (MCSAM) to derive the exact CDF and MCSs. We expect that the MCSAM will easily identify the plant's vulnerabilities to review the exact MCSs consistent with CDF results without additional post-processing or Monte Carlo Simulation.

Editorial for the Special Issue on “Fault Trees and Attack Trees: Extensions, Solution Methods, and Applications”

Fault Trees are well-known models for the reliability analysis of systems, used to compute several kinds of qualitative and quantitative measures, such as minimal cut-sets, system failure probability, sensitivity (importance) indices, etc [...]

An Improved FFIP Method Based on Mathematical Logic and SysML

In recent years, the model-based safety analysis (MBSA) has been developing continuously. The Functional Failure Identification and Propagation (FFIP) method is a graphics processing technology which supports the analysis of fault propagation paths before making costly design commitments. However, the traditional FFIP has some deficiencies. In this paper, we extend the functional failure logic (FFL) in the FFIP and introduce the concept of deviation. So, FFIP can be used to analyze the failure process of the systems and make the logical analysis of functional failure easier. Based on the extended FFL, we present a new overview of the FFIP. The FFIP is improved by using mathematical logic and Systems Modeling Language (SysML). The standard expression of FFL is realized, which is conducive to the subsequent modeling and modification. Additionally, we use the failure logic analysis in the FFIP to improve the state machine diagram (SMD) in SysML. Finally, the improved FFIP method is used to analyze the fault propagation paths of the system and Simulink is used for simulation. The fault tree is generated according to the simulation results, the minimum cut set is calculated, and the key failure parts of the system are obtained.

A Method to Avoid Underestimated Risks in Seismic SUPSA and MUPSA for Nuclear Power Plants Caused by Partitioning Events

Seismic probabilistic safety assessment (PSA) models for nuclear power plants (NPPs) have many non-rare events whose failure probabilities are proportional to the seismic ground acceleration. It has been widely accepted that minimal cut sets (MCSs) that are calculated from the seismic PSA fault tree should be converted into exact solutions, such as binary decision diagrams (BDDs), and that the accurate seismic core damage frequency (CDF) should be calculated from the exact solutions. If the seismic CDF is calculated directly from seismic MCSs, it is drastically overestimated. Seismic single-unit PSA (SUPSA) models have random failures of alternating operation systems that are combined with seismic failures of components and structures. Similarly, seismic multi-unit PSA (MUPSA) models have failures of NPPs that undergo alternating operations between full power and low power and shutdown (LPSD). Their failures for alternating operations are modeled using fraction or partitioning events in seismic SUPSA and MUPSA fault trees. Since partitioning events for one system are mutually exclusive, their combinations should be excluded in exact solutions. However, it is difficult to eliminate the combinations of mutually exclusive events without modifying PSA tools for generating MCSs from a fault tree and converting MCSs into exact solutions. If the combinations of mutually exclusive events are not deleted, seismic CDF is underestimated. To avoid CDF underestimation in seismic SUPSAs and MUPSAs, this paper introduces a process of converting partitioning events into conditional events, and conditional events are then inserted explicitly inside a fault tree. With this conversion, accurate CDF can be calculated without modifying PSA tools. That is, this process does not require any other special operations or tools. It is strongly recommended that the method in this paper be employed for avoiding CDF underestimation in seismic SUPSAs and MUPSAs.

Reliability tracking method of power system equipment based on Embedded Internet of things technology

Power equipment is one of the most important transmission and transformation equipment in power system. Improving the reliability of power equipment is of great significance to the safe and reliable operation of the whole power grid. A reliability tracking method of power system equipment based on Embedded Internet of things technology is proposed. The minimum cut set algorithm of reliability index based on Embedded Internet of things technology is given. In this paper, a fault tree analysis method for power system equipment unreliability index is proposed. According to the analysis of equipment structure, component function and failure mode, the fault tree model of power system equipment is established, and the reliability tracking calculation example is analyzed. Experiments show that the method can track the order stably, determine the key components that affect the reliability of the equipment, and identify the weak links of the equipment.

Model-based Safety Assessment of a Triple Modular Generator with xSAP

Abstract The system design process needs to cope with the increasing complexity and size of systems,motivating the replacement of labor intensivemanual techniques with automated and semi-automated approaches.Recently, formal methods techniques, such as model-based verification and safety assessment, have been increasingly used to model systems under fault and to analyze them, generating artifacts such as fault trees and FMEA tables. In this paper, we show how to apply model-based techniques to a realistic case study from the avionics domain: a high integrity power distribution system, the Triple Modular Generator (TMG). The TMG is composed of a redundant and reconfigurable plant and a controller that must guarantee a high level of reliability. The case study is a significant challenge, from the modeling perspective, since it implements a complex reconfiguration policy, specified via a number of requirements in natural language, including a set of mutually dependent and potentially conflicting priority constraints. Moreover, from the verification standpoint, the controller must be able to handle an exponential number of possible faulty configurations. Our contribution is twofold. First, we formalize and validate the requirements and, using a constraint-based modeling style, we synthesize a correct by construction controller, avoiding the enumeration of all possible fault configurations, as is currently done by manual approaches. Second, we describe a comprehensive methodology and process, supported by the xSAP safety analysis platform that targets the modeling and safety assessment of faulty systems. Using xSAP, we are able to automatically extract minimal cut sets for the TMG. We demonstrate the scalability of our approach by analyzing a parametric version of the TMG case study that contains more than 700 variables and 90 faults.

The scenario modeling of regional competitiveness risks based on the Chapman-Kolmogorov equations

The paper is devoted to the development of analytical tools for assessing the dynamics of risks to the competitiveness of Russian regions within the conditions of incomplete information. The choice of analysis methods for assessing the risk dynamics was substantiated. A solution based on the implementation of homogeneous Markov models with a discrete set of states and continuous time was proposed, it allowed to assess the probability of risks affecting regional competitiveness. A hierarchical structure of factors that determine the risks of regional competitiveness was formed as a cause-and-effect graph. Corresponding systems of Kolmogorov – Chapman differential equations were obtained and solved. An example for analyzing a 3-element minimal cut set of a cause-effect graph was presented. A set of scenarios for the study of risks and their combinations in various conditions was proposed. The solution was obtained for three leading Russian regions. For a set of scenarios, numerical assessments of risk factors that significantly affect the decline in the competitiveness of regions have been fulfilled. The study results made it possible to rank the effects of critical event occurrence, to identify the most significant risk factors for the loss of sustainable development and competitiveness for the Russian Federation regions.

Risk assessment of ice dams for water diversion projects based on fuzzy fault trees

Ice dams are among the important risks affecting the operational safety and water conveyance efficiency of water diversion projects in northern China. However, no evaluation indicator system for ice dam risk assessment of water diversion projects has been proposed. Therefore, in this paper, based on the formation mechanism of ice dams, the risk assessment indicator system and the possibility calculation model of ice dams were both proposed for water diversion projects based on the fuzzy fault tree analysis method. The ice dam risk fault tree constructed in this study mainly includes three aspects: ice production, ice transport, and ice submergence conditions. Eighteen basic risk indicators were identified, and 72 minimum cut sets were obtained by using the mountain climb method. Eight risk indicators were determined as the key risk indicators for ice dams, including meteorological conditions, narrowed cross section, sluice incident, erroneous scheduling judgment, ice cover influence, flat bed slope, control structures, and ice flow resistance of piers. Then, the canal from the Fenzhuanghe sluice to the Beijumahe sluice of the Middle Route of the South-to-North Water Diversion Project was taken as the research object. Combined with the expert scoring method, the ice dam risk probability of the canal was determined to be 0.2029 × 10−2, which was defined as a level III risk, which is an occasionally occurring risk. The study results can support ice dam risk prevention and canal system operation in winter for water diversion projects.

Fault Tree Analysis Using Bayesian Optimization: A Reliable and Effective Fault Diagnosis Approaches

Fault tree analysis (FTA) is a powerful technique that can be used to analyze the faults related to a large-scale complicated system. In the conventional FTA, it can be used to assess the effects of combinations of failures on system behavior but the ambiguities and uncertainties of basic events cannot be handled effectively. Therefore, employing Bayesian theory helps probabilistic estimation of basic events and subsequently the top event. This study presents an integrated approach to Bayesian theory and FTA for handling uncertainty in the fault diagnosis of heavy CNC machines. In this context, making use of a directed graph to describe the fault, and then expressed as reachability matrix, the fault tree and fault information are obtained. In order to set the determinate conditions at every node of fault tree combining FTA with rule reasoning, the minimal cut sets are determined by representing the fault tree as a top-down logical equation. Finally, Bayesian method is integrated into the fault tree diagnostic method to calculate the posterior probability triggered by each fault tree to locate where on the fault tree and ensure high efficiency of fault diagnosis. The proposed methodology is applied to the fault diagnosis of fuzzy probabilistic analysis in the Φ 160 CNC boring and milling machine. The results indicate that the proposed approach is very reliable and effective in fault diagnosis considering uncertainty reduction or handling.

Reliability analysis of ballast cleaning device based on fuzzy FTA and FMEA

On the basis of analyzing the fault tree diagram of the ballast cleaning device of railway switch ballast cleaning machine, the fuzzy fault tree of the ballast cleaning device is established by blurring the probability of bottom event. Introducing grey fuzzy analysis correlation method, using the normal fuzzy comprehensive evaluation method of combining the theory and experts, quantitative and qualitative analysis, the fuzzy fault tree based on fault tree’s minimum cut sets, the fuzzy importance degree of the basic events, calculation of each failure mode and the top event correlation, figure out the influence of the top event to occur to the larger events and failure mode. Then FMEA method is used to analyze the key parts of ballast cleaning device such as gripper and sprocket, and corresponding compensation measures are put forward according to the specific failure reasons.

Study on the multi-objective optimization of reliability and operating cost for natural gas pipeline network

The development of natural gas pipeline network towards larger scale and throughput has urged better reliability of the pipeline network to satisfy transportation requirement. Previously, studies of optimizing natural gas pipeline network have been mainly focused on reducing operating cost, with little concern on the reliability of pipeline network. For a natural gas pipeline network with a variety of components and complicated topology, a multi-objective optimization model of both reliability and operating cost is proposed in this study. Failure of each component and the state of pipeline network under failure conditions are taken into account, and minimum cut set method is employed to calculate the reliability of the pipeline network. The variables to be determined for the optimization objectives are the rotating speed of compressors and the opening of valves. Then the solving procedure of the proposed model is presented based on Decoupled Implicit Method for Efficient Network Simulation (DIMENS) method and NS-saDE algorithm. The validity of the optimization model is ascertained by its application on a complicated pipeline network. The results illustrate that the optimization model can depict the relative relationship between reliability and operating cost for different throughput, by which the operation scheme with both satisfying reliability and operating cost can be obtained. In addition, the customer reliability and the impact of the failure of each pipeline on the whole network can be evaluated quantitatively to identify the consumers and pipelines of maintenance priority. The pipeline network reliability can be improved through proper monitoring and maintenance of these consumers and pipelines.

A method for transformation from dynamic fault tree to binary decision diagram

Dynamic fault tree (DFT) is a powerful modeling approach for reliability analysis of complex system with dynamic failure behaviors. In reality, the tree structure may be highly coupled either by shared basic events or by the high-level dynamic gates. Currently, the application of sequential binary decision diagram (SBDD)-based method for quantitative analysis of such highly coupled DFTs is mainly limited to DFTs whose dynamic gates locate in the bottom of the tree. Moreover, there is no efficient way dealing with the dependencies among different nodes of a SBDD 1-path. This paper makes an improvement to the SBDD-based approach. A generation procedure is proposed to directly construct the binary decision diagram (BDD) model for a DFT with arbitrary tree structure. During the construction, the sequential-dependent information of the tree is derived as several BDD nodes, each indicates a binary-sequential event representing the sequence of two occurred basic events. A topological sorting is applied on each 1-path of the resultant BDD to obtain its contained disjoint cut sequences. Based on this, both qualitative and quantitative analysis can be performed on the DFT with no limitations on tree structure, and its minimal cut sequence set (CSS) is obtained as disjoint. Examples are provided for verification and comparison, and the results illustrate the merits of the proposed approach.