Traditional Fault Tree Research Articles

Bayesian network approach for dynamic fault tree with common cause failures and interval uncertainty parameters

Traditional fault tree analysis often assumes that the basic events are independent and the failure parameters are known. Therefore, it is powerless to deal with the correlation among basic events and the uncertainty of failure parameters due to the small failure data. Therefore, a framework based on continuous-time Bayesian network is proposed to evaluate the reliability of fault tree with common cause failures (CCF) and uncertainty parameters. Firstly, the best-worst method (BWM) and hesitant fuzzy set (HFS) are introduced to address the issue of β-factor being influenced by experts’ subjectivity. Then, the interval theory is introduced to deal with the uncertainty parameters. Based on continuous-time Bayesian network, the conditional probability functions of logic gates (i.e. AND gate, OR gate, spare gate, priority AND gate) with CCF are derived, and the upper and lower bounds of failure probability of top event can be solved. Finally, the fault tree of CPU system is given to verify the effectiveness of the proposed framework.

Risk assessment of man‐machine systems under safety‐critical multitasking situations

AbstractMultitasking is increasingly common in highly complex and safety‐critical systems, especially under abnormal situations. Mental overload (MOL) may occur and result in forgetting/mistaking tasks uncertainly. Such probabilistic errors could have catastrophic consequences and contribute greatly to the multitasking risk of man‐machine systems. In this paper, to better identify the risks of safety‐critical multitasking situations, MOL mechanism is investigated and a risk analysis method considering MOL is proposed. MOL occurs when the demand for resources estimated by Multiple Resources Model exceeds an operator's ability. Then, the operator's performance degrades, and s/he tends to mistake or abandon parts of tasks. Based on the MOL mechanism, a MOL‐performance dependency (MOL‐PDEP) gate is proposed to incorporate MOL into risk analysis. Its inputs are concurrent tasks, and it triggers the related hazardous human behavior events with certain probabilities if MOL occurs. Through this gate, the dependence among these events and their nondeterministic cause relationships to MOL are added to traditional fault tree (FT), which presents a challenge issue to FT analysis. An implicit method is proposed to analyze the FT with MOL‐PDEP gate and calculate the accident probability. A case study on a helicopter crash accident demonstrates the effectiveness of the proposed method.

Fault Tree Analysis Including Component Dependencies

Fault Tree (FT) analysis is not only the most common technique used in engineering practice for the estimation of system reliability, but is also a key tool shared between designers, analysts, and regulators for the safe operation and licensing purposes. In spite of its long lasting success, traditional FT analysis presents significant limitations in modeling a wide range of features frequently encountered in modern systems. The most critical of these is the assumption of failure events independence, which is often not justified by the realistic behavior of the engineering system, undermining modeling accuracy. This article introduces a novel methodology for the analysis of FTs allowing for component dependencies and dynamic features. The proposed approach, based on the use of binary decision diagrams, is demonstrated using a simple numerical application for verification. Its applicability and computational feasibility is discussed in details.

Risk Analysis of Autonomous Underwater Vehicle Operation in a Polar Environment Based on Fuzzy Fault Tree Analysis

Autonomous underwater vehicles have long been used in marine explorations, and their application in recent polar expeditions is particularly noteworthy. However, the complexity and extreme conditions of the polar environment pose risks to the stable operation of autonomous underwater vehicles. This study adopted the methodology of fuzzy fault tree analysis to deeply analyze the operational risks of autonomous underwater vehicles in polar environments. While traditional fault tree analysis maps the causal relationships and probabilities between basic and intermediate events, fuzzy fault tree analysis models the uncertainty of data and determines the failure probability by integrating expert opinions. This study revealed that polar environment-induced failures play a more substantial role in autonomous underwater vehicle loss in polar regions than inherent system failures. The study identified ‘recovery failure’ and ‘poor communication’ as the major risk factors facing autonomous underwater vehicles in polar environments, exhibiting the highest failure probabilities. Specifically, among various polar environmental factors, ‘large ice concentration’, ‘ice thickness’, and ‘roughness of ice underside’ under ‘bad’ conditions were found to have a significant impact on the autonomous underwater vehicle’s failure probability. The fuzzy fault tree analysis method in this study successfully filled the gap created by the absence of historical data by effectively incorporating expert opinions, enabling a quantitative presentation of the impact of polar environments, which has been previously difficult to convey in qualitative terms.

Reliability Evaluation of Complex Nuclear Energy Redundancy Systems with Atypical Time-Distribution Events

In complex nuclear energy redundancy systems, there are many failure events that do not follow specific time distribution. For these atypical time-distribution events, traditional dynamic fault tree (DFT) methods cannot be applied directly, which has posed great challenges to reliability modeling and evaluating. In this contribution, we summarize atypical time-distribution events in nuclear energy redundancy systems and propose new modeling and evaluating methods based on DFT. To demonstrate the reasonability of the proposed methods, two case studies about make-up water pumps and emergency diesel generators are analyzed in comparison with traditional DFT. The results indicate that the proposed methods can effectively model and analyze the reliability of redundant systems with atypical time-distribution events. The proposed methods can provide useful information for optimization design of nuclear energy redundancy systems and has potential to improve the economy of nuclear power plants by relaxing overestimated unreliability.

Optimization of Leakage Risk and Maintenance Cost for a Subsea Production System Based on Uncertain Fault Tree

Traditional fault tree analysis is an effective tool used to evaluate system risk if the required data are sufficient. Unfortunately, the operation and maintenance data of some complex systems are difficult to obtain due to economic or technical reasons. The solution is to invite experts to evaluate some critical aspect of the performance of the system. In this study, the belief degrees of the occurrence of basic events evaluated by experts are measured by an uncertain measure. Then, a system risk assessment method based on an uncertain fault tree is proposed, based on which two general optimization models are established. Furthermore, the genetic algorithm (GA) and the nondominated sorting genetic algorithm II (NSGA-II) are applied to solve the two optimization models, separately. In addition, the proposed risk assessment method is applied for the leakage risk evaluation of a subsea production system, and the two general optimization models are used to optimize the leakage risk and maintenance cost of the subsea production system. The optimization results provide a theoretical basis for practitioners to guarantee the safety of subsea production system.

Application of Nonlinear Triangular Fuzzy Fault Tree Algorithm in Predicting Lithium Battery Air Transport Accidents

The traditional triangular fuzzy fault tree prediction model adopts the linear approximation method. Therefore, the accident prediction error is large. Based on the analysis of the error sources and the fuzzy set, the precise calculation method of the event at the top of the fault tree is given. By using the numerical calculation software, an accurate calculation method of nonlinear triangular fuzzy accident prediction was adopted to predict lithium battery air transport fire accidents, and the fuzzy importance of the cause event was calculated.

Automatic Generation of Event Trees and Fault Trees: A Model-Based Approach

In the past few decades, the increasing complexity of modern engineering systems has been driven by the integration of a large number of components whose operations may involve many disciplines (e.g., thermal hydraulics, plant operations, cybersecurity). Most computational tools used by industry and regulators for system safety and reliability assessments are still based on the traditional fault tree (FT) and event tree (ET) approach, which may not be able to capture complex interactions among system constituents. The use of simulation tools has widely increased in the past few decades to improve the fidelity of the reliability and safety analyses. However, the direct use of simulation tools as part of dynamic probabilistic risk assessment (DPRA) methods is not getting traction since (1) modeling the whole system under consideration with DPRA methods may be computationally expensive and unnecessary, and (2) the manual integration of DPRA models into existing state-of-practice probabilistic risk assessment models (i.e., based on FTs and ETs) can be time consuming and prone to errors. In this paper we propose a procedure to overcome this limitation by presenting several algorithms designed to automatically construct subsystem ETs and FTs from DPRA methods for integration into an existing ET/FT system model.

Research on Failure Diagnosis Method of a Rocket Borne Micro Electro-Mechanical Systems Recorder Based on Fault Tree

With the complexity and diversification of rocket launch tasks, more stringent requirements are put forward for MEMS electronic equipment, which is closely related to the stability and security of rocket. The key components of the rocket-borne electronic system are composed of discrete components, integrated components and corresponding connected fixed components. The selection, welding and board level connection of each electronic element determine the reliability of the MEMS component. In this paper, the fault tree analysis method is applied to the reliability analysis of the rocket-borne recorder, and the dynamic fault tree analysis method is introduced to compensate the deficiency of the traditional static fault tree analysis method, finally the simulation comparison with Monte-Carlo analysis method is carried out to verify the effectiveness and feasibility of the proposed method. The work of this paper is of great significance for establishing the reliability theory of the system and mastering the experience of quick failure diagnosis.

Research on Fault Tree Reconstruction Based on Contingency

The fault tree analysis (FTA) method is an important analysis method for safety system engineering. Traditional accident analysis theory agrees that basic events lead to top events, but it does not fully consider that the accident process is accidental, and the calculation results exaggerate the probability of accident occurrence. This paper selects typical collision accidents, analyzes the shortcomings of the existing fault tree, indicates that there is a contingency in the accident process, constructs a probability fault tree based on the traditional fault tree, and puts forward concepts of “probability AND gate” and “probability OR gate”. In addition, based on the traditional quantitative analysis method of fault trees, calculations of the occurrence probability, probability importance coefficient, and critical importance coefficient of top events are modified, and the modified quantitative calculation is applied to accident cases.

Rapid Fault Diagnosis Method of Elevator System Based on Multiattribute Decision Making

Fault tree analysis is often used in elevator fault diagnosis because of its simplicity and reliability. However, the traditional fault tree method has the problems of low efficiency due to ignoring location change of bottom events during troubleshooting. This paper proposes a rapid diagnosis method based on multiattribute decision making to solve the problem. The fault tree of the elevator system is constructed based on expert knowledge and multisource data, and the location-related matrix is constructed according to the complex vertical structure of the elevator. Then, the attributes of bottom events such as the failure probability, search cost, location time cost, and location-related attributes are comprehensively analyzed in this paper. Finally, the TOPSIS method for dynamic attributes is used based on the work above to achieve the optimal troubleshooting sequence of elevator vibration fault. The results show that the proposed method is more efficient when compared to the optimal troubleshooting sequence obtained by the traditional method.

Damage assessment for large-scale surface warship systems using a dynamic location damage tree model quantified based on the multilevel Monte Carlo simulation

The multiple functions of large-scale surface warship systems involve the main system, subsystems and important components with complex logical relationships, and some components require a number of redundant components to maintain their high reliability. Moreover, the information about the ship structure, system and equipments cannot be fully determined in practical naval battlefield, especially locations of some key components. Therefore, it is difficult to accurately perform damage assessment of large-scale surface warships using traditional fault tree models. Monte Carlo simulation (MCS) is the most robust method for damage assessment, but it is computationally demanding. To address the issue, a new method with high efficiency and accuracy is proposed herein. In the proposed method, a dynamic damage tree (DLDT) model is developed to describing complex ship systems with redundant and uncertain information, and the multilevel Monte Carlo (MLMC) simulation is modified to reduce the computational cost of MCS. The modified MLMC is capable of obtaining the damage probabilities of various components, subsystems and top events for different numbers of anti-ship weapons. Results of numerical validation demonstrate that the computational cost of the proposed MLMC is much less than that of MCS while achieving the same accuracy level. By combining DLDT and MLMC, the proposed method provides a reference for efficiently and accurately assessing the functional damage to large-scale surface warships.

Reliability Analysis of Special Vehicle Critical System Using Discrete-Time Bayesian Network

The reliability assessment of special vehicles has become very important. However, due to the special structure of special vehicles, it is difficult to collect a large amount of experimental data. The use of traditional fault tree analysis cannot accurately assess product reliability. In this paper, dynamic fault trees are used to model the critical systems of special vehicles, and discrete Bayesian networks are used to evaluate the reliability of critical systems of special vehicles, which solved the problems of difficulty in accurately describing complex systems in the process of system reliability analysis and difficulty in obtaining accurate data in the process of analysis. Finally, through the combination of expert experience and the evaluation of the calculation results, the rationality of the method used in this paper in the reliability evaluation of special vehicles is verified.

Satellite Dynamic Fault Analysis Method Based on AltaRica Logic Modeling

Modern spacecraft has developed into a complex system integrated multi-task, multi-specialty and multi-information. The cross-linking and coupling between different systems have exposed more and more logic sequence fault caused by non-software and hardware failures. It is difficult to comprehensively and accurately analyze the logical sequence faults of complex systems by using traditional fault tree analysis (FTA), failure mode and effect analysis (FMEA) and other manual methods. Furthermore, the reliability and safety of the spacecraft cannot be effectively guaranteed. In this paper, the dynamic fault analysis of the spacecraft was carried out based on the method of AltaRica logic modeling. The satellite power supply and distribution (PSD) subsystem was taken as an example. A dynamic model of charge and discharge between the solar array, the storage battery and the bus was established. Logical events and sequences of the bus power supply fault was calculated. The results show that this method can effectively complete the dynamic modeling and fault analysis of the spacecraft system, and it has higher analysis capability and efficiency than traditional methods.

Dynamic Modeling of Reactor Protection System in Nuclear Power Plant for Reliability Evaluation Based on State Transition Diagram

Reliability assessment of a digital dynamic system using traditional Fault Tree Analysis (FTA) is difficult. This paper addresses the dynamic modeling of safety-critical complex systems such as the digital Reactor Protection System (RPS) in Nuclear Power Plants (NPPs). The digital RPS is a safety system utilized in the NPPs for safe operation and shut-down of the reactor in emergency events. A quantitative evaluation reliability analysis for the digital RPS with 2-out-of-4 architecture using the state transition diagram is presented in this paper. The study assesses the effects of independent hardware failures, Common Cause Failures (CCFs), and software failures on the failure of the RPS through calculating Probability of Failure on Demand (PFD). The results prove the validity of the proposed method in analyzing and evaluating reliability of the digital RPS and also show that the CCFs and longer detection time are the main contributions to the PFD of digital RPS.

Dynamic Modeling of Reactor Protection System in Nuclear Power Plant for Reliability Evaluation Based on State Transition Diagram

Reliability assessment of a digital dynamic system using traditional Fault Tree Analysis (FTA) is difficult. This paper addresses the dynamic modeling of safety-critical complex systems such as the digital Reactor Protection System (RPS) in Nuclear Power Plants (NPPs). The digital RPS is a safety system utilized in the NPPs for safe operation and shut-down of the reactor in emergency events. A quantitative evaluation reliability analysis for the digital RPS with 2-out-of-4 architecture using the state transition diagram is presented in this paper. The study assesses the effects of independent hardware failures, Common Cause Failures (CCFs), and software failures on the failure of the RPS through calculating Probability of Failure on Demand (PFD). The results prove the validity of the proposed method in analyzing and evaluating reliability of the digital RPS and also show that the CCFs and longer detection time are the main contributions to the PFD of digital RPS.

Reliability evaluation of integrated detritiation system for fusion reactors based on DBDT approach

Integrated detritiation system (IDS) would play a key role in controlling the tritium release and atmosphere cleanup under accident scenarios in fusion reactors, and thus it is very significant to evaluate and ensure its reliability. Up to now, many conceptual designs for IDS have been developed worldwide, yet few are focused on its reliability studies. Due to complex redundant designs and functional dependence, this system has notable temporal failure behaviors that traditional static fault trees (SFT) are unavailable to capture and evaluate. In this contribution, motivated to understand the effect of temporal failure behaviors on reliability of IDS, dynamic fault trees (DFT) are first to be adopted to study its reliability through using dynamic binary decision tree (DBDT) approach. The results show the reliability indexes for IDS calculated by DFTs are one to two times lower than those obtained by traditional SFT, which means some overly conservative reliability requirements on IDS could be relaxed. The results also demonstrate that the DFT-based reliability evaluation method would be of great help for the fusion energy system’s optimization design in the future.

Gas pipeline failure evaluation method based on a Noisy-OR gate bayesian network

We propose a method based on the Noisy-OR gate Bayesian network to address cases of insufficient sample data. First, a fault tree model of gas pipelines was established. Mapping this model to the Bayesian network (BN), the failure probability was 0.074 according to a traditional BN and fault tree analysis (FTA). By applying the Noisy-OR gate to determine the conditional probability of related nodes, the failure probability of the system was 0.058. Compared with FTA and the BN, this approach could more precisely determine minimum cut sets and diagnose risky factors. The combination of the BN and a Noisy-OR gate is an alternative method for evaluating the reliability of gas pipelines, and this approach can provide a relatively realistic analysis in other evaluation fields because it considers other influencing factors. The findings of this study can aid decision-making and prevent accidents from occurring.

Quantitative FTA using Monte Carlo analyses in a pharmaceutical plant

The evaluation of faults in a multipurpose pharmaceutical pilot plant used for production of polymer particles was performed, integrating traditional Fault Tree Analyses (FTA) and Monte Carlo procedures and employing tools of the quality risk management methodology for production of medicines. The plant was divided into four basic processes: (i) receipt and sampling of materials; (ii) treatment of purified water; (iii) reaction; and (iv) lyophilization and purification. For each process, the most critical failure was selected, and the FTA was built. Selection of basic events considered the most important effects on the final quality of the medicine. Then, the FTA was reduced to basic events using Boolean algebra. The quantitative assessment was made by assigning failure rate values for each event. The reliability data of the failure rates were based on the literature that deals with similar processes. The frequencies for each fault were determined through Monte Carlo simulations, considering that fault probability distributions followed the exponential distribution. When failure rate (ʎ) data are available, the quality management can establish a prediction of plant behavior over a period. This scenario is consistent and coherent with practices of pharmaceutical sites, since occurrence of high rates of failure must be corrected immediately in order to preserve the safety of the operation.

System Reliability Estimation of Divert Attitude Control System of a Launch Vehicle using Bayesian Networks

Divert attitude and control system (DACS) is a one-shot system and provides attitude correction and translation of the Launch vehicle. DACS consists of many flight critical sub systems which are arranged in a series configuration. The traditional Reliability block diagram and Fault tree diagram methods are unsuitable for reliability modelling, when considering uncertainty among the components and system. Bayesian network is the natural choice to model dependencies among the components and system. DACS being one shot system, it is very expensive and time consuming to test more number of systems during the design and development. Hence the data is drawn from component level, subsystem level and expert opinion is used for reliability estimation. In this paper, Bayesian network modelling of DAC system was carried out for estimating the reliability using multi-level data. An algorithm is developed for computation of Conditional probabilities in Bayesian network. Posterior probability distribution of components is calculated using Markov Chain Monte Carlo (MCMC) simulations and results are compared with Junction tree based exact inference algorithm. MATLAB code is developed to estimate the reliability of DAC system.