Computerized fault tree construction for a train braking system

A new approach for fault tree automation is proposed which is a hybrid of the digraph and decision table methods, using the best features of both. The new method is based on the flexibility of the decision table method but incorporates a way of detecting, classifying and analysing control loops, similar to the use of operators in the digraph approach. As well as using operators to deal with control loops, a new operator is introduced that deals with electrical circuits. This means that when constructing the fault trees, difficulties of handling repeated events are eliminated and the size of the fault trees is significantly reduced. The method has been tested by its application to a braking system on a train. © 1997 John Wiley & Sons, Ltd.     

A fast BDD algorithm for large coherent fault trees analysis

Although a binary decision diagram (BDD) algorithm has been tried to solve large fault trees until quite recently, they are not efficiently solved in a short time since the size of a BDD structure exponentially increases according to the number of variables. Furthermore, the truncation of If–Then–Else (ITE) connectives by the probability or size limit and the subsuming to delete subsets could not be directly applied to the intermediate BDD structure under construction. This is the motivation for this work.This paper presents an efficient BDD algorithm for large coherent systems (coherent BDD algorithm) by which the truncation and subsuming could be performed in the progress of the construction of the BDD structure. A set of new formulae developed in this study for AND or OR operation between two ITE connectives of a coherent system makes it possible to delete subsets and truncate ITE connectives with a probability or size limit in the intermediate BDD structure under construction. By means of the truncation and subsuming in every step of the calculation, large fault trees for coherent systems (coherent fault trees) are efficiently solved in a short time using less memory. Furthermore, the coherent BDD algorithm from the aspect of the size of a BDD structure is much less sensitive to variable ordering than the conventional BDD algorithm.     

Posbist fault tree analysis of coherent systems

When the failure probability of a system is extremely small or necessary statistical data from the system is scarce, it is very difficult or impossible to evaluate its reliability and safety with conventional fault tree analysis (FTA) techniques. New techniques are needed to predict and diagnose such a system's failures and evaluate its reliability and safety. In this paper, we first provide a concise overview of FTA. Then, based on the posbist reliability theory, event failure behavior is characterized in the context of possibility measures and the structure function of the posbist fault tree of a coherent system is defined. In addition, we define the AND operator and the OR operator based on the minimal cut of a posbist fault tree. Finally, a model of posbist fault tree analysis (posbist FTA) of coherent systems is presented. The use of the model for quantitative analysis is demonstrated with a real-life safety system.     

How dependent basic events with interval-valued probabilities affect fault tree analysis

This paper studies the effect of the dependence state between basic events (BEs) on fault tree analysis (FTA) when the probabilities of events are characterized by interval values. The well-known Frèchent bounds are extended for modeling six different types of dependence states between BEs. Three indices, called average dependence effect (ADE), location effect (LE) and size effect (SE), are defined for evaluating the effect of the dependence states between BEs on the probability of top event (TE) and identifying influential and non-influential dependence states. Then, the proposed method is applied to fault tree (FT) examples, thereby explaining the dependence problem in FTA. To further verify the practicability of the method, FTA of the unilateral asymmetric movement failure of an aircraft flap mechanism is performed. The results show that: (i) the opposite and negative dependence contribute to the reliability of a parallel system while the perfect and positive dependence reduce it, (ii) the perfect and positive dependence contribute to the reliability of a series system while the opposite and negative dependence reduce it, and (iii) parallel systems are more reliable than series systems regardless of the dependence between BEs.     

Efficient Ordering Heuristics in Binary Decision Diagram–based Fault Tree Analysis

In binary decision diagram–based fault tree analysis, the size of binary decision diagram encoding fault trees heavily depends on the chosen ordering. Heuristics are often used to obtain good orderings. The most important heuristics are depth‐first leftmost (DFLM) and its variants weighting DFLM (WDFLM) and repeated‐event‐priority DFLM (RDFLM). Although having been used widely, their performance is still only vaguely understood, and not much formal work has been done. This article firstly identifies some basic requirements for a reliable benchmark and gives a benchmark generation method. Then, using the generated benchmark, the performance of DFLM and its variants is studied. Both the experimental results and some interesting findings for our research questions are proposed. This article also presents a new weighting DFLM (NWDFLM) heuristic and the underlying basic ideas and gives both the experimental results and conclusions on the performance comparison. As a final synthesis of all previous results, a practical suggestion of the order of heuristic selection to process a large fault tree is NWDFLM < WDFLM < RDFLM. Copyright © 2012 John Wiley & Sons, Ltd.     

A simple component-connection method for building binary decision diagrams encoding a fault tree

A simple new method for building binary decision diagrams (BDDs) encoding a fault tree (FT) is provided in this study. We first decompose the FT into FT-components. Each of them is a single descendant (SD) gate-sequence. Following the node-connection rule, the BDD-component encoding an SD FT-component can each be found to be an SD node-sequence. By successively connecting the BDD-components one by one, the BDD for the entire FT is thus obtained. During the node-connection and component-connection, reduction rules might need to be applied. An example FT is used throughout the article to explain the procedure step by step.Our method proposed is a hybrid one for FT analysis. Some algorithms or techniques used in the conventional FT analysis or the newer BDD approach may be applied to our case; our ideas mentioned in the article might be referred by the two methods.     

An efficient real‐time method of analysis for non‐coherent fault trees

Fault tree analysis is commonly used to assess the reliability of potentially hazardous industrial systems. The type of logic is usually restricted to AND and OR gates, which makes the fault tree structure coherent. In non‐coherent structures not only components' failures but also components' working states contribute to the failure of the system. The qualitative and quantitative analyses of such fault trees can present additional difficulties when compared with the coherent versions. It is shown that the binary decision diagram (BDD) method can overcome some of the difficulties in the analysis of non‐coherent fault trees. This paper presents the conversion process of non‐coherent fault trees to BDDs. A fault tree is converted to a BDD that represents the system structure function (SFBDD). An SFBDD can then be used to quantify the system failure parameters but is not suitable for the qualitative analysis. Established methods, such as the meta‐products BDD method, the zero‐suppressed BDD (ZBDD) method and the labelled BDD (L‐BDD) method, require an additional BDD that contains all prime implicant sets. The process using some of the methods can be time consuming and is not very efficient. In addition, in real‐time applications the conversion process is less important and the requirement is to provide an efficient analysis. Recent uses of the BDD method are for real‐time system prognosis. In such situations as events happen, or failures occur, the prediction of mission success is updated and used in the decision‐making process. Both qualitative and quantitative assessments are required for the decision making. Under these conditions fast processing and small storage requirements are essential. Fast processing is a feature of the BDD method. It would be advantageous if a single BDD structure could be used for both the qualitative and quantitative analyses. Therefore, a new method, the ternary decision diagram (TDD) method, is presented in this paper, where a fault tree is converted to a TDD that allows both qualitative and quantitative analyses and no additional BDDs are required. The efficiency of the four methods is compared using an example fault tree library. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures

Many real-life fault-tolerant systems are subjected to sequence-dependent failure behavior, in which the order in which the fault events occur is important to the system reliability. Such systems can be modeled by dynamic fault trees (DFT) with priority-AND (pAND) gates. Existing approaches for the reliability analysis of systems subjected to sequence-dependent failures are typically state-space-based, simulation-based or inclusion-exclusion-based methods. Those methods either suffer from the state-space explosion problem or require long computation time especially when results with high degree of accuracy are desired. In this paper, an analytical method based on sequential binary decision diagrams is proposed. The proposed approach can analyze the exact reliability of non-repairable dynamic systems subjected to the sequence-dependent failure behavior. Also, the proposed approach is combinatorial and is applicable for analyzing systems with any arbitrary component time-to-failure distributions. The application and advantages of the proposed approach are illustrated through analysis of several examples.     

基于事故树的海岛爆破飞石风险辨识

为帮助海岛爆破工程科学系统化的作业,运用事故树分析法对海岛爆破飞石事故的产生原因进行了分析,建立了爆破飞石事故树图,求出最小割集13个,最小径集8个,得到了基本事件的重要结构度值。结果表明:爆破方案审核不严、现场管理不当等问题是造成海岛爆破飞石事故的主要原因,针对这些基本事件提出了4点预防爆破飞石事故的对策措施,为今后的海岛工程爆破系统作业提供了决策支持。     

基于事故树的海岛爆破飞石风险辨识

为帮助海岛爆破工程科学系统化的作业,运用事故树分析法对海岛爆破飞石事故的产生原因进行了分析,建立了爆破飞石事故树图,求出最小割集13个,最小径集8个,得到了基本事件的重要结构度值。结果表明:爆破方案审核不严、现场管理不当等问题是造成海岛爆破飞石事故的主要原因,针对这些基本事件提出了4点预防爆破飞石事故的对策措施,为今后的海岛工程爆破系统作业提供了决策支持。     

基于故障树的计算机安全性分析模型

提出了通过分析计算机系统的资源实体、访问者权限、安全需求和弱点等安全属性,按照不同的安全需求构造出安全故障树来直观地反映攻击者可能选取的攻击手段的安全状况评价方法;分析安全故障树,使用潜在攻击路径和系统安全失效概率从定性和定量两个方面表达计算机系统的安全状况,为系统的安全改进提供指导和建议。     

Condition-based fault tree analysis (CBFTA): A new method for improved fault tree analysis (FTA), reliability and safety calculations

Condition-based maintenance methods have changed systems reliability in general and individual systems in particular. Yet, this change does not affect system reliability analysis. System fault tree analysis (FTA) is performed during the design phase. It uses components failure rates derived from available sources as handbooks, etc. Condition-based fault tree analysis (CBFTA) starts with the known FTA. Condition monitoring (CM) methods applied to systems (e.g. vibration analysis, oil analysis, electric current analysis, bearing CM, electric motor CM, and so forth) are used to determine updated failure rate values of sensitive components. The CBFTA method accepts updated failure rates and applies them to the FTA. The CBFTA recalculates periodically the top event (TE) failure rate (λ_TE) thus determining the probability of system failure and the probability of successful system operation—i.e. the system's reliability.FTA is a tool for enhancing system reliability during the design stages. But, it has disadvantages, mainly it does not relate to a specific system undergoing maintenance.CBFTA is tool for updating reliability values of a specific system and for calculating the residual life according to the system's monitored conditions. Using CBFTA, the original FTA is ameliorated to a practical tool for use during the system's field life phase, not just during system design phase.This paper describes the CBFTA method and its advantages are demonstrated by an example.     

基于动态故障树的CTCS-3级ATP系统可靠性分析简

 针对传统的可靠性分析方法分析CTCS-3级ATP系统动态失效问题的不足,提出采用动态故障树分析其可靠性。首先,分析系统的结构和功能建立动态故障树模型;其次,采用深度优先最左遍历算法搜索动态故障树模型,得到独立的子树;最后,在引入可修系统可靠性指标基础上,采用解析法和马尔科夫矩阵迭代法求解子树,结合分层迭代方法对动态故障树分析法改进,以减小运算量,使得上述可靠性指标能用于CTCS-3级ATP系统的可靠性评估。计算所得可靠性指标与可靠性框图分析得到的结果对比表明：动态故障树能够更好地描述系统的冗余性和容错性等特点,提高了可靠性指标的精度。     

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.     

基于事故树分析的露天爆破飞散物预防研究

为了防止露天爆破飞散物事故的发生,确保爆破施工安全,根据露天爆破作业流程,分析了爆破飞散物产生原因,建立了事故树模型,在此基础上进行了定性分析,求出事故树最小割集为15个,最小径集为4个;得到了结构重要度排序,提出了爆破飞散物事故的对策措施,可为今后的爆破设计、施工和安全管理提供参考。     

A new reliability evaluation method for networks with imperfect vertices using BDD

As an efficient data structure for representation and manipulation of Boolean functions, binary decision diagrams (BDDs) have been applied to network reliability analysis. However, most of the existing BDD methods on network reliability analysis have assumed perfectly reliable vertices, which is often not true for real‐world networks where the vertices can fail because of factors such as limited resources (eg, power and memory) or harsh operating environments. Extensions have been made to the existing BDD methods (particularly, edge expansion diagram and boundary set–based methods) to address imperfect vertices. But these extended methods have various constraints leading to problems in accuracy or space efficiency. To overcome these constraints, in this paper, we propose a new BDD‐based algorithm called ordered BDD dependency test for K‐terminal network reliability analysis considering both edge and vertex failures. Based on a newly defined concept “dependency set”, the proposed algorithm can accurately compute the reliability of networks with imperfect vertices. In addition, the proposed algorithm has no restrictions on the starting vertex for the BDD model construction. Comprehensive examples and experiments are provided to show effectiveness of the proposed approach.     

Approximate estimation of system reliability via fault trees

In this article, we show how fault tree analysis, carried out by means of binary decision diagrams (BDD), is able to approximate reliability of systems made of independent repairable components with a good accuracy and a good efficiency. We consider four algorithms: the Murchland lower bound, the Barlow-Proschan lower bound, the Vesely full approximation and the Vesely asymptotic approximation. For each of these algorithms, we consider an implementation based on the classical minimal cut sets/rare events approach and another one relying on the BDD technology. We present numerical results obtained with both approaches on various examples.     

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。     

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。