Finding minimal cut sets in a fault tree

This paper presents a new method for identification of minimal cut sets in a fault tree. The (non-minimal) cut sets are found by a modification of the well-known MOCUS algorithm. These cut sets are stored in a virtual tree structure which requires far less core space than the MOCUS cut set matrix. The minimal cut sets are found by traversing this virtual tree a number of times. In the first cycle, all cut sets of order one are identified. In the next cycle, all cut sets of order two are identified and compared with the cut sets of order one to exclude non-minimal stes. This procedure is continued until all minimal cut sets are identified. The procedure is very fast. Compared to the standard MOCUS program the computer time is reduced by at least a factor of ten.     

Fault tree truncation error bounds

The solution of large fault trees can only performed if cut sets of a high order or low probability are neglected. This procedure is non-pessimistic since possible contributions to the top gate failure probability are ignored. Since the number of cut sets neglected is generally large, it is possible that their total contribution is significant compared to the total probability of those cut sets included in the evaluation of the top gate failure probability.In this paper a practical method for the estimation of upper bounds on the total failure probability of cuts sets of a given order is presented. This allows bounds on the contribution of all the cut sets neglected through cut-off procedures in fault tree solutions to be calculated, and so validate the top event failure probability. The method given here is much superior to that suggested by Modarres and Dezfuli in that it produces much lower and hence more useful bounds. The method of Modarres and Dezfuli can be refined, but for realistic fault tree examples the method given here always gives the least pessimistic and most practical bounds.     

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。     

Computation of minimal cut sets of fault trees: Experiences with three different methods

There are several different methods by which the minimal cut sets of a given fault tree can be computed. In this paper we shall discuss and compare three such methods. Two analytical methods, a bottom-up and a top-down algorithm, and a simulative method will be considered. Finally, a new analytical algorithm for the evaluation of the minimal cut sets is proposed.     

液氧贮槽爆炸事故树分析

采用安全系统工程的方法 ,对液氧贮槽爆炸进行了事故树分析 ,通过求事故树最小割集 ,进行结构重要度分析 ,从而对液氧贮槽爆炸的事故原因进行分析、预测 ,并提出了相应的预防控制措施     

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。     

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。     

Development of measures to estimate truncation error in fault tree analysis

The fault tree quantification uncertainty from the truncation error has been of great concern for the reliability evaluation of large fault trees in the probabilistic safety analysis (PSA) of nuclear plants. The truncation limit is used to truncate cut sets of the gates when quantifying the fault trees. This paper presents measures to estimate the probability of the truncated cut sets, that is, the amount of truncation error. The functions to calculate the measures are programmed into the new fault tree quantifier FTREX (Fault Tree Reliability Evaluation eXpert) and a Benchmark test was performed to demonstrate the efficiency of the measures.The measures presented in this study are calculated by a single quantification of the fault tree with the assigned truncation limit. As demonstrated in the Benchmark test, lower bound of truncated probability (LBTP) and approximate truncation probability (ATP) are efficient estimators of the truncated probability. The truncation limit could be determined or validated by suppressing the measures to be less than the assigned upper limit. The truncation limit should be lowered until the truncation error is less than the assigned upper limit. Thus, the measures could be used as an acceptability of the fault tree quantification results. Furthermore, the developed measures are easily implemented into the existing fault tree solvers by adding a few subroutines to the source code.     

一种新的模拟电路故障模糊集确定算法

提出了一种在模拟电路故障诊断中故障类模糊集的确定算法．该算法基于测前仿真法,不但同时适用于线性电路和非线性电路,而且可以确定元件模糊组以外的故障类模糊集．算法利用电路仿真故障特征数据计算故障的类间差异矩阵,从而完成故障类模糊集的确定．计算示例验证了该算法的有效性．     

A new hybrid method for fault tree analysis

This paper describes a new method for determining the significant minimal cut sets of complex fault trees. It can be classified as hybrid, being based on the application of both Top Down and Bottom Up reduction approaches. This solution has been adopted particularly to accurately estimate the truncation error when the probabilistic cut-off technique is applied. Experimental results on real fault trees proved that the degree of conservatism of the truncation error is negligible at any practical combination of the probabilistic and logical threshold values.This new fault tree analysis procedure has been implemented, in C language, in the second version of the computer programme ISPRA-FTA.     

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.     

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.     

露天深孔爆破导爆管起爆网路盲炮事故树分析

为避免露天深孔爆破导爆管起爆网路产生盲炮,确保爆破施工安全,按照露天深孔爆破作业流程,通过分析导爆管起爆网路盲炮产生原因,建立了事故树模型。并在此基础上进行了定性分析,求出事故树最小割集为32个,最小径集为4个。得到了结构重要度排序,提出了盲炮事故预防的对策措施,可为类似工程的爆破设计、施工和安全管理提供参考。     

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。     

Element substitution algorithm for general two-terminal network reliability analyses

The computation of the reliability of two-terminal networks is a classical reliability problem. For these types of problems, one is interested, from a general perspective, in obtaining the probability that two specific nodes can communicate. This paper presents a holistic algorithm for the analysis of general networks that follow a two-terminal rationale. The algorithm is based on a set replacement approach and an element inheritance strategy that effectively obtains the minimal cut sets associated with a given network. The vast majority of methods available for obtaining two-terminal reliability are generally based on assumptions about the performance of the network. Some methods assume network components can be in one of two states: (i) either completely failed; or (ii) perfectly functioning, others usually assume that nodes are perfectly reliable and thus, these methods have to be complemented or transformed to account for node failure, and the remaining methods assume minimal cut sets can be readily computed in order to analyze more complex network and component behavior. The algorithm presented in this paper significantly differs from previous approaches available in the literature in the sense that it is based on a predecessor matrix and an element substitution technique that allows for the exact computation of minimal cut sets and the immediate inclusion of node failure without any changes to the pseudo-code. Several case networks are used to validate and illustrate the algorithms.     

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。     

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.     

Computation of joint reliability importance of two gate events in a fault tree

Joint reliability importance (JRI) of two gate events (GEs) is investigated along with its properties in a fault tree (FT). Computation of JRI of two GEs involves complexity because statistical dependency between GEs exists as a result of replication of basic events (BEs). To avoid complexity in computing the JRI, the topological relationships of two GEs in a FT are identified and classified into three classes. The explicit formula for the JRI of the two GEs is derived. JRI for each class is shown to be computed by using a conventional FT algorithm. By illustrating min. cut set representation of the bridge network, it is also shown that the degree of relationship between two min. cut sets can be measured by the JRI of the corresponding two GEs.