Improved accuracy in quantitative fault tree analysis

The fault tree diagram defines the causes of the system failure mode or ‘top event’ in terms of the component failures and human errors, represented by basic events. By providing information which enables the basic event probability to be calculated, the fault tree can then be quantified to yield reliability parameters for the system. Fault tree quantification enables the probability of the top event to be calculated and in addition its failure rate and expected number of occurrences. Importance measures which signify the contribution each basic event makes to system failure can also be determined. Owing to the large number of failure combinations (minimal cut sets) which generally result from a fault tree study, it is not possible using conventional techniques to calculate these parameters exactly and approximations are required. The approximations usually rely on the basic events having a small likelihood of occurrence. When this condition is not met, it can result in large inaccuracies. These problems can be overcome by employing the binary decision diagram (BDD) approach. This method converts the fault tree diagram into a format which encodes Shannon's decomposition and allows the exact failure probability to be determined in a very efficient calculation procedure. This paper describes how the BDD method can be employed in fault tree quantification. © 1997 John Wiley & Sons, Ltd.     

基于模糊故障树的军用气象物资包装可靠性分析

应用模糊故障树分析方法对军用气象物资包装可靠性进行了系统分析,简要介绍了模糊故障树分析方法的基本理论,利用专家判断和模糊集理论相结合的方法,评估了故障树底事件发生的模糊失效概率。并以"TFS-1通风干湿表包装"为例,建立了包装系统的故障树,采用下行法求解了引起顶事件发生的最小割集,定量分析计算,得出模糊失效率为0.0705,同时计算了各底事件的重要度。模糊故障树分析方法对于提高军用气象物资包装防护能力,确保物资装备质量,具有非常重要的意义。     

硝铵炸药真空干燥工艺燃爆事故致灾因素的研究

真空干燥是硝铵炸药生产过程中一道容易发生燃爆事故的重要工序。为研究硝铵炸药真空干燥过程中发生燃爆事故的原因及机理，通过事故案例分析和现场调研，确定了导致燃爆事故的各个基本事件及其逻辑关系，并由此构建以燃爆事故作为顶事件的事故树。采用布尔代数化简事故树，得到87个最小割集和9个最小径集，结果显示每个最小径集包含的基本事件都较多，说明真空干燥工艺安全性较低。通过计算各基本事件的结构重要度并排序，得到结构重要度较大的基本事件，由此推断出导致燃爆事故的主要基本事件，并有针对性地提出相应的改进措施与建议，为企业的安全生产提供参考。     

A PSA-based vital area identification methodology development

This paper presents a vital area identification method based on the current probabilistic safety assessment (PSA) techniques. The vital area identification method in this paper is focused on core melt rather than radioactive material release. Furthermore, it describes a conceptual framework with which the risk from sabotage-induced events could be assessed.Location minimal cut sets (MCSs) are evaluated after developing a core melt location fault tree (LFT). LFT is a fault tree whose basic events are sabotage-induced damages on the locations within which various safety-related components are located. The core melt LFT is constructed by combining all sequence LFTs of various event trees with OR gates. Each sequence LFT is constructed by combining the initiating event LFT and the mitigating event LFTs with an AND gate. The vital area could be identified by using the location importance measures on the core melt location MCSs. An application was made to a typical 1000 MWe pressurized water reactor power plant located at the Korean seashore.The methodology suggested in the present paper is believed to be very consistent and most complete in identifying the vital areas in a nuclear power plant because it is based on the well-proven PSA technology.     

Quantification of Highly Coupled Dynamic Fault Tree Using IRVPM and SBDD

Dynamic fault tree (DFT) is a commonly used method to model systems having sequence‐dependent and function‐dependent failure behaviors. The failure structure function of a DFT can be expressed by logic OR of all minimal cut sequences, that is, minimal cut sequence set (MCSS). The occurrence probability to the top event of a DFT can be calculated using inclusion–exclusion (IE) principle based on enumerating the MCSS. However, the IE‐based approach would have exponential evaluation complexity. Then, a sequential binary decision diagram (SBDD)‐based method is proposed and successfully applied to analyze simple dynamic systems. This method is more efficient than IE‐based method in asymptotic analysis. But this method cannot handle complex systems modeled by different highly coupled dynamic gates. In this paper, we put forward using Independent Random Variable Probabilistic Model‐based plus SBDD‐based methods to quantify an MCSS to obtain the failure probability of a complex DFT. The results obtained by the proposed method are exactly matched with those obtained by the existing methods. In addition, this method enhances the analyzing ability of the original SBDD and retains the advantage of high computational efficiency. The application and advantage of our proposed method is demonstrated by a case study. Copyright © 2014 John Wiley & Sons, Ltd.     

On the numerical solution of fault trees

In this paper an account will be given of the numerical solution of the logic trees directly extracted from the Recursive Operability Analysis. Particular attention will be devoted to the use of the NOT and INH logic gates for correct logical representation of Fault Trees prior to their quantitative resolution.The NOT gate is needed for correct logical representation of events when both non-intervention and correct intervention of a protective system may lead to a Top Event.The INH gate must be used to correctly represent the time link between two events that are both necessary, but must occur in sequence. Some numerical examples will be employed to show both the correct identification of the events entering the INH gates and how use of the AND gate instead of the INH gate leads to overestimation of the probability of occurrence of a Top Event.     

On simplification of large fault trees

This paper describes some fault tree optimization algorithms used in STUK PSA code SPSA that is capable of generating minimal cut sets for fault trees containing 12 000 gates and basic events. The complexity of a minimal cut set search is a function of multiple gates and basic events. In a fault tree containing 1000 multiple elements, these optimizations reduce the number of multiple elements often by 30 to 50%. One novel feature of the algorithm is that no boolean reduction rules are used, since the fault tree itself contains its simplification rules.     

基于FTA的老年人APP交互设计

目的提升老年人对APP的满意度,帮助老年人更好地接受和使用APP。方法提出基于故障树分析(FTA)的老年人APP交互设计方法。首先通过焦点小组确定导致错误发生的原因并建立故障树,对错误发生的原因进行合理分类;随后对故障树进行定性定量分析,计算故障树的最小切集和错误发生的概率,找到导致头号事件发生的核心因素;接着进行重要度分析,计算构造重要度,根据构造重要度值对引起错误发生的基本事件进行排序,为设计改良提供理论上的优先顺序;最后以老年人医疗APP为研究案例进行设计改良,并对改良后的结果进行错误率验证。结论该方法可以有效地发现老年人操作APP时出现障碍的原因,不仅可以帮助设计师找到较为合理的改良方案,而且还可以使老年人获得良好的交互体验。     

Fault Diagnosis Improvement Using Dynamic Fault Model in Optimal Sensor Placement: A Case Study of Steam Turbine

Health data are collected dominantly through sensors mounted on different locations in the system. Optimization of sensor network has a significant influence on the reliability of system health prognostics process. In this research, the effect of sensors reliability is studied on their placement optimization. Sensors are considered in this study as components in system failure model. This study is aimed to use ‘Priority AND’ gate for evaluating the effect of time dependencies of sensors as well as components failure on the optimal sensor placement. Because of that, PAND gate is added to the fault tree between all sensors and their corresponding components to develop the failure model of each sensor placement scenario. For calculating the probability of top event, a Monte Carlo‐based algebraic approach is proposed. In algebraic approach, temporal operator ‘BEFORE’ is proposed for calculating the probability of ‘PAND’ gate. The result of using ‘BEFORE’ operator is an analytical solution for probability of each cut sequence. Because of the complexity of analytical solution in practical problems, a Monte Carlo simulation is utilized on the solution in this research. Then the probability of each cut sequence is calculated. Consequently, the probability of top event for each scenario is obtained. Finally, all scenarios are ranked based on top event probabilities. As a case study, optimization of sensor placement has been demonstrated on steam turbine and results are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

A practical method for accurate quantification of large fault trees

This paper describes a practical method to accurately quantify top event probability and importance measures from incomplete minimal cut sets (MCS) of a large fault tree. The MCS-based fault tree method is extensively used in probabilistic safety assessments. Several sources of uncertainties exist in MCS-based fault tree analysis. The paper is focused on quantification of the following two sources of uncertainties: (1) the truncation neglecting low-probability cut sets and (2) the approximation in quantifying MCSs. The method proposed in this paper is based on a Monte Carlo simulation technique to estimate probability of the discarded MCSs and the sum of disjoint products (SDP) approach complemented by the correction factor approach (CFA). The method provides capability to accurately quantify the two uncertainties and estimate the top event probability and importance measures of large coherent fault trees. The proposed fault tree quantification method has been implemented in the CUTREE code package and is tested on the two example fault trees.     

Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment

Traditional fault tree (FT) analysis is widely used for reliability and safety assessment of complex and critical engineering systems. The behavior of components of complex systems and their interactions such as sequence- and functional-dependent failures, spares and dynamic redundancy management, and priority of failure events cannot be adequately captured by traditional FTs. Dynamic fault tree (DFT) extend traditional FT by defining additional gates called dynamic gates to model these complex interactions. Markov models are used in solving dynamic gates. However, state space becomes too large for calculation with Markov models when the number of gate inputs increases. In addition, Markov model is applicable for only exponential failure and repair distributions. Modeling test and maintenance information on spare components is also very difficult. To address these difficulties, Monte Carlo simulation-based approach is used in this work to solve dynamic gates. The approach is first applied to a problem available in the literature which is having non-repairable components. The obtained results are in good agreement with those in literature. The approach is later applied to a simplified scheme of electrical power supply system of nuclear power plant (NPP), which is a complex repairable system having tested and maintained spares. The results obtained using this approach are in good agreement with those obtained using analytical approach. In addition to point estimates of reliability measures, failure time, and repair time distributions are also obtained from simulation. Finally a case study on reactor regulation system (RRS) of NPP is carried out to demonstrate the application of simulation-based DFT approach to large-scale problems.     

A fault tree analysis strategy using binary decision diagrams

The use of binary decision diagrams (BDDs) in fault tree analysis provides both an accurate and efficient means of analysing a system. There is a problem, however, with the conversion process of the fault tree to the BDD. The variable ordering scheme chosen for the construction of the BDD has a crucial effect on its resulting size and previous research has failed to identify any scheme that is capable of producing BDDs for all fault trees. This paper proposes an analysis strategy aimed at increasing the likelihood of obtaining a BDD for any given fault tree, by ensuring the associated calculations are as efficient as possible. The method implements simplification techniques, which are applied to the fault tree to obtain a set of ‘minimal’ subtrees, equivalent to the original fault tree structure. BDDs are constructed for each, using ordering schemes most suited to their particular characteristics. Quantitative analysis is performed simultaneously on the set of BDDs to obtain the top event probability, the system unconditional failure intensity and the criticality of the basic events.     

A New Ordering Method of Basic Events in Fault Tree Analysis

The ordering of basic events is critical to fault tree analysis on the basis of binary decision diagrams (BDDs). Many attempts have been made to seek an efficient ordering result with the aim of reducing the complexity of BDD. In this article, a new ordering method, namely, priority ordering method, is proposed. The new method takes into account not only the effects of the layers of fault tree but also the repeated events, the neighboring events, and the number of events under the same gate. According to these four effects, the priorities that sort the basic events of the fault tree are defined. The new method inherits the merits of structure‐based and weight‐based methods. It is able to evaluate the basic events on the basis of the structure‐based method and the size of the subtree on the basis of the weighted‐based method. Demonstrated by the examples, the proposed priority ordering method is superior to the existing ordering methods in terms of reducing the nodes in the BDD and improving the efficiency in transforming a fault tree to a BDD. Copyright © 2011 John Wiley & Sons, Ltd.     

数字电路可测性设计的一种故障定位方法

在逻辑函数ReedMuller模式的电路可测性设计方面，文章采用AND门阵列和XOR门树结构来设计电路，提出了一种设计方案，可实现任意逻辑函数的功能，而且所得电路具有通用测试集和完全可故障定位的特点。给出了进行故障定位的方法，并可把它应用于其他相关电路的可测性设计。     

基于FTA模型的荔枝冷藏运输环节风险分析

目的解决荔枝冷藏运输环节中安全风险识别及定性分析的难题。方法基于因素空间及故障树分析模型(FTA),分析荔枝冷链运输环节的安全事件集、空间结构(工位)集和简约因素集,建立荔枝冷藏运输环节风险因素关系矩阵,通过矩阵运算获取不同空间结构下荔枝运输安全事故发生的基本事件。结果根据运算求解结果,构建荔枝运输环节的故障树模型,获取了运输环节故障树的最小割集。荔枝冷藏运输事故最小割集数为13个,并分析了各个基本事件的结构重要度。结论通过研究最小割集及事件的结构重要度,进行荔枝冷链运输环节的安全分析,并提出了促进现场安全管理的对策及建议。     

Fuzzy Fault Diagnosis of a Diesel Engine Non-start

The diesel locomotive plays an important role in the field of transport,and the engine maintenance work is the prerequisite and guarantee for the locomotive normal working.In this paper,we first establish the fault tree model of locomotive engine 16V240ZJ on the basis of engine non-start as the top event.Then we combines the fuzzy mathematics theory and fault tree analysis method for failure diagnosis of 16V240ZJ engine's abnormal start-up.We obtained the fuzzy probability curve and top events probability c...     

基于梯形模糊数的数控磨床砂轮架系统故障树分析

数控磨床砂轮架系统故障树分析中的一大难点是确定基本事件的发生概率,基本事件的发生情况存在模糊性且由于时间和成本的限制往往无法通过实验获得足够的可靠性数据。为了解决这一问题,引入模糊集合论,用梯形模糊数来描述故障树分析中的基本事件和顶事件的发生概率。首先对数控磨床砂轮架系统的结构层次进行分析,建立砂轮架系统的故障树。然后以砂轮架系统主轴振动异响为例进行模糊故障树分析,求解顶事件发生概率的梯形模糊数;并类比传统故障树分析中"临界重要度"的概念,定义适用于模糊故障树分析的"模糊临界重要度"。最后根据求解的模糊临界重要度对基本事件进行排序,确定危害程度较高的基本事件,结果与企业的实际情况相符合。结果表明该方法能够有效解决数控磨床故障树分析中基本事件难于准确赋值的问题,为企业提高机械系统的可靠性提供了一种定量依据。     

基于FMEA和FTA的老年人汽车人机界面交互设计研究

目的 提升老年人汽车界面满意度,设计适合老年人使用的汽车界面.方法 提出基于失效模式与效应分析(FMEA)、故障树分析(FTA)的研究方法,首先成立会议小组进行SHERPA分析,绘制汽车界面层次任务分析图;随后运用FMEA找出汽车界面中的潜在失效模式,计算风险优先数值;接着选取风险优先数值高的失效模式,运用FTA寻找其发生的原因,对其以图形化表示;再对故障树进行定性定量分析,计算故障树的最小切集和失效事件发生概率,找到失效发生的核心因素;最后对失效事件进行改良并对改良后的结果进行验证.结论 以老年人汽车界面为例进行研究,该方法可以有效发现老年人操作汽车界面发生错误的原因,不仅可以帮助设计师找到改良的重点,还可以使老年人获得良好的驾驶体验.     

A recursive, time-averaged approach for fault tree quantitative analysis

A new approach in fault tree quantitative analysis, based essentially on the recursive evaluation of time-averaged reliability parameters associated with a fault tree, is presented. The methodology is a complete one covering the following problems: the evaluation of averaged unavailabilities or unreliabilities, failure and repair rates and failure and repair intensities associated with the basic events involved in a fault tree, the evaluation of unavailability or unreliability, occurrence rates and occurrence intensities associated with the top event of a fault tree, evaluation of the importance and sensitivity associated with basic events, and implicants according to different definitions. At this stage in the development of the methodology the common cause failures are not considered. Although in practice the presented algorithms have shown, in the cases of large fault trees, difficulties related to the computing speed and memory capabilities of present personal computers, the methodology remains valuable, at least by the new theoretical results.     

基于事故树的深孔爆破边坡稳定性分析

为了能够对爆破后形成的露天边坡稳定性进行合理的分析评价,结合大小鱼山岛露天爆破边坡失稳的情况,采用事故树分析方法,建立了工程爆破现场露天边坡失稳事故树模型。计算出事故树的最小割集96个,最小径集3个以及基本事件的结构重要度系数,并得到基本事件结构重要度排序,找出了导致边坡失稳的主要原因是边坡监测和边坡支护。然后根据基本事件结构重要度的排序,制定合理有序的预防措施。事故树分析方法可以全面阐述露天矿边坡失稳的各种因素和逻辑关系,并通过对结构重要性分析,提出合理预防措施,为爆破露天边坡的安全管理提供参考依据。