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.     

Quantification of sequential failure logic for fault tree analysis

Fault tree analysis (FTA) is generally accepted as an efficient method for analyzing system failures. It is well known that a fault tree (FT) is equivalent to a minimal cut set fault tree with all minimal cut-AND structures. The minimal cut-AND structure is an AND conjunction of an output and all inputs that compose a minimal cut set. For the structure, the failed state of the output becomes true when all failed states of inputs exist simultaneously. There are cases where the output of the minimal cut-AND structure depends not only on all failed states of inputs but also on the sequence of occurrences of those failures. This sequential failure logic (SFL) is equivalently expressed with Priority-AND gates in FTA, where inputs to the gates have constant failure and repair rates. A probabilistic model for analysis of SFL was proposed and equations with multiple integration for arbitrary number of inputs were derived from the model. However, it is usually difficult to solve the multiple integration when the number of inputs exceeds a certain range. This paper presents analytical solutions of the probability that the output is in a failed state at time t and the statistically expected number of failures of the output per unit time at time t for the special case where inputs are characterized by common failure and repair rates. In addition, the analysis of FT involving SFL is demonstrated by means of software Mathematica.     

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.     

Hybrid fault tree analysis using fuzzy sets

In conventional fault tree analysis (FTA), the ambiguous and imprecise events such as human errors tend not to be handled effectively. To overcome this disadvantage, a hybrid approach employing fuzzy set evaluation and probabilistic estimation for FTA is proposed to evaluate abnormal events. The safety problem of unexpected robot motion in an aircraft wing drilling system was analyzed using the proposed method. The results indicated that the proposed approach is very effective in analyzing the reliability of a man-machine system.     

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.     

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.     

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。     

Graphical fault tree analysis for fatal falls in the construction industry

The current study applied a fault tree analysis to represent the causal relationships among events and causes that contributed to fatal falls in the construction industry. Four hundred and eleven work-related fatalities in the Taiwanese construction industry were analyzed in terms of age, gender, experience, falling site, falling height, company size, and the causes for each fatality. Given that most fatal accidents involve multiple events, the current study coded up to a maximum of three causes for each fall fatality. After the Boolean algebra and minimal cut set analyses, accident causes associated with each falling site can be presented as a fault tree to provide an overview of the basic causes, which could trigger fall fatalities in the construction industry. Graphical icons were designed for each falling site along with the associated accident causes to illustrate the fault tree in a graphical manner. A graphical fault tree can improve inter-disciplinary discussion of risk management and the communication of accident causation to first line supervisors.     

Combining task analysis and fault tree analysis for accident and incident analysis: A case study from Bulgaria

Understanding the reasons for incident and accident occurrence is important for an organization's safety. Different methods have been developed to achieve this goal. To better understand the human behaviour in incident occurrence we propose an analysis concept that combines Fault Tree Analysis (FTA) and Task Analysis (TA). The former method identifies the root causes of an accident/incident, while the latter analyses the way people perform the tasks in their work environment and how they interact with machines or colleagues. These methods were complemented with the use of the Human Error Identification in System Tools (HEIST) methodology and the concept of Performance Shaping Factors (PSF) to deepen the insight into the error modes of an operator's behaviour. HEIST shows the external error modes that caused the human error and the factors that prompted the human to err. To show the validity of the approach, a case study at a Bulgarian Hydro power plant was carried out. An incident – the flooding of the plant's basement – was analysed by combining the afore-mentioned methods. The case study shows that Task Analysis in combination with other methods can be applied successfully to human error analysis, revealing details about erroneous actions in a realistic situation.     

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.     

Application of the fault tree analysis for assessment of power system reliability

A new method for power system reliability analysis using the fault tree analysis approach is developed. The method is based on fault trees generated for each load point of the power system. The fault trees are related to disruption of energy delivery from generators to the specific load points. Quantitative evaluation of the fault trees, which represents a standpoint for assessment of reliability of power delivery, enables identification of the most important elements in the power system. The algorithm of the computer code, which facilitates the application of the method, has been applied to the IEEE test system. The power system reliability was assessed and the main contributors to power system reliability have been identified, both qualitatively and quantitatively.     

故障树分析法在某型飞机火控系统故障诊断中的应用

故障树分析法是系统安全、可靠性分析研究中常用的一种方法。基于故障树分析法与专家系统相结合的某型飞机火控系统故障诊断仪,以机载火控系统不工作为顶事件,建立了故障树,并对故障树作了定性分析,本系统不但具有故障诊断能力,还具有较强的自学习的功能。结果表明,故障树分析法是机载火控系统故障诊断的一种有效方法。     

Quantitative analysis of a fault tree with priority AND gates

A method for calculating the exact top event probability of a fault tree with priority AND gates and repeated basic events is proposed when the minimal cut sets are given. A priority AND gate is an AND gate where the input events must occur in a prescribed order for the occurrence of the output event. It is known that the top event probability of such a dynamic fault tree is obtained by converting the tree into an equivalent Markov model. However, this method is not realistic for a complex system model because the number of states which should be considered in the Markov analysis increases explosively as the number of basic events increases. To overcome the shortcomings of the Markov model, we propose an alternative method to obtain the top event probability in this paper. We assume that the basic events occur independently, exponentially distributed, and the component whose failure corresponds to the occurrence of the basic event is non-repairable. First, we obtain the probability of occurrence of the output event of a single priority AND gate by Markov analysis. Then, the top event probability is given by a cut set approach and the inclusion–exclusion formula. An efficient procedure to obtain the probabilities corresponding to logical products in the inclusion–exclusion formula is proposed. The logical product which is composed of two or more priority AND gates having at least one common basic event as their inputs is transformed into the sum of disjoint events which are equivalent to a priority AND gate in the procedure. Numerical examples show that our method works well for complex systems.     

Development and evaluation of an uncertainty importance measure in fault tree analysis

In a fault tree analysis, an uncertainty importance measure is used to identify those basic events that significantly contribute to the uncertainty of the top-event probability. This paper defines an uncertainty importance measure of a basic event or of a group of basic events, and develops a two-stage procedure for experimentally evaluating the measure under the assumption that the probability of each basic event follows a lognormal distribution. The proposed method utilizes the Taguchi tolerance design technique with modifications. Then, the so-called contribution ratios which evaluate the main and/or interaction effects of the uncertainties of log-transformed basic-event probabilities on the uncertainty of the log-transformed top-event probability are calculated. The contribution ratios are used to estimate the defined uncertainty importance measure of a basic event or of a group of basic events. The proposed method consists of two stages for computational efficiency. In the first stage, the basic events with negligible effects on the uncertainty of the log-transformed top-event probability are screened out, and more detailed analyses are conducted in the second stage with a substantially smaller number of basic events. In addition, this paper presents an analysis method to quantify the percentage reduction in the uncertainty of the log-transformed top-event probability when the uncertainty of each basic-event probability is reduced.     

Efficient algorithms to assess component and gate importance in fault tree analysis

One of the principal activities of risk assessment is either the ranking or the categorization of structures, systems and components with respect to their risk-significance or their safety-significance. Several measures, so-called importance factors, of such a significance have been proposed for the case where the support model is a fault tree. In this article, we show how binary decision diagrams can be use to assess efficiently a number of classical importance factors. This work completes the preliminary results obtained recently by Andrews and Sinnamon, and the authors. It deals also with the concept of joint reliability importance.     

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。     

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.     

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。     

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.