A dynamic fault tree

The fault tree analysis is a widely used method for evaluation of systems reliability and nuclear power plants safety. This paper presents a new method, which represents extension of the classic fault tree with the time requirements. The dynamic fault tree offers a range of risk informed applications. The results show that application of dynamic fault tree may reduce the system unavailability, e.g. by the proper arrangement of outages of safety equipment. The findings suggest that dynamic fault tree is a useful tool to expand and upgrade the existing models and knowledge obtained from probabilistic safety assessment with additional and time dependent information to further reduce the plant risk.     

The classification and regression tree approach to pump failure rate analysis

In this article, a technique based on rule induction is suggested as non-parametric alternative to determine the expected failure rates of 143 centrifugal pumps included in a oil refinery plant and subjected to different operating conditions. At the same time, the procedure makes it possible to determine the critical operating factors influencing the reliability of the pumps. In particular, the classification and regression tree approach is used to automatically generate rules from an extended data base of the plant concerning information about failures and operating conditions of the different facilities.     

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.     

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.     

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.     

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.     

A branching search approach to safety system design optimisation

Safety systems are designed to prevent or mitigate the consequences of potentially hazardous events. In many industries the failure of such systems can result in fatalities. Current design practice is usually to produce a safety system which meets a target level of performance that is deemed acceptable by the regulators. However, when the system failure will result in fatalities it is desirable for the system to achieve an optimal rather than adequate level of performance given the limitations placed on available resources.The unavailability of safety systems can be predicted using fault tree analysis methods. Formulating an optimisation problem for the system design has features which make standard mathematical optimisation techniques inappropriate. The form of the objective function is itself a function of the design variables, the design variables are mainly integers and the constraint forms can be implicit or non-linear.This paper presents a Branching Search algorithm which exploits characteristics common to many safety systems to explore the potential design space and deliver an optimal design. Efficiency in the method is maintained by performing the system unavailability evaluations using the Binary Decision Diagram method of fault tree solution. Limitations are placed on resources such as cost, maintenance down-time and spurious trip frequency. Its application is demonstrated on a High Integrity Protection System.     

Dot chart analysis as a means to develop a fault tree: application to a catalytic hydrogenation unit

This paper describes the application of dot chart analysis to a semicontinuous catalytic hydrogenation unit. Dot chart tables have been used as a basis for developing the recursive operability analysis and the fault trees (FTs), whose aim is to determine the safety of both the unit and its operators. The unit is formed of two reactors in parallel: the transfer of operations from one reactor to the other when its catalyst is exhausted is performed by means of the isolation systems installed for this purpose on the inlet and outlet lines. FTs assessed the expected number of leak at 3×10⁻³ occurrences per mission time. The study clearly showed that the operations could be regarded as safe, since, with minor modification to control system and operative procedure, these leaks would be of pressurised nitrogen and hence without consequences for the unit and its operators.     

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。     

A hybrid approach for identification of root causes and reliability improvement of a die bonding process—a case study

This paper presents an industrial case study on reliability improvement of the die bonding machine in the semiconductor industry. A hybrid approach combining dynamic analysis, process decomposition, and a structured fault tree was used to analyze the die bonding process. Firstly, the process was analyzed technically and decomposed into several stages according to different motions. Then, the die movement and force balance at each stage were analyzed according to physical laws, to identify the root causes of die rotation. A structured fault tree was then constructed to trace all possible causes and effects. A qualitative approach was used to identify critical events (root causes) for further analysis. Experiments were conducted to modify the bonding process to reduce the effects of the critical events. Finally, further process modification was proposed for simplification of the fault tree. This case study combined the knowledge in control and reliability engineering and presented a hybrid approach, which is very useful for practising engineers.     

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 new approach to the d-MC problem

Many real-world systems (such as cellular telephones, transportation, etc.) are multistate-node acyclic network (MNAN) composed of multistate-nodes. Such network has a source node (position) where the signal source is located, a number of sink nodes that only receive the signal, and a number of intermediate nodes that retransmit the received signal to some other nodes. The non-sink node has different states determined by a set of nodes receiving the signal directly from it. The reliability of MNAN can be computed in terms of minimal trees (MTs). Based on the Branch-and-Bound algorithm, we developed an intuitive algorithm that is simpler than the best-known existing method. The computational complexity of the proposed algorithm is also analyzed. One example is illustrated to show how all MTs are generated by the proposed algorithm. The reliability of this example is then computed.     

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.     

可靠性理论在建筑爆破拆除抑尘分析中的应用

在对广州市旧体育馆爆破拆除的抑尘系统进行可靠性评价时,应用了可靠性理论。本文简介了该工程抑尘系统的构成,概述了该系统故障树的构建。通过计算,得出了基本事件的重要度次序。同时,分析了理论结果与实际结果不同的原因。文章认为,运用可靠性理论有助于决策者全面了解抑尘系统的情况和找出主要矛盾,减少系统失效的可能性。     

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 rule induction approach to improve Monte Carlo system reliability assessment

A Decision Tree (DT) approach to build empirical models for use in Monte Carlo reliability evaluation is presented. The main idea is to develop an estimation algorithm, by training a model on a restricted data set, and replacing the Evaluation Function (EF) by a simpler calculation, which provides reasonably accurate model outputs. The proposed approach is illustrated with two systems of different size, represented by their equivalent networks. The robustness of the DT approach as an approximated method to replace the EF is also analysed. Excellent system reliability results are obtained by training a DT with a small amount of information.     

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     

Fault diagnostics of dynamic system operation using a fault tree based method

For conventional systems, their availability can be considerably improved by reducing the time taken to restore the system to the working state when faults occur. Fault identification can be a significant proportion of the time taken in the repair process. Having diagnosed the problem the restoration of the system back to its fully functioning condition can then take place. This paper expands the capability of previous approaches to fault detection and identification using fault trees for application to dynamically changing systems. The technique has two phases. The first phase is modelling and preparation carried out offline. This gathers information on the effects that sub-system failure will have on the system performance. Causes of the sub-system failures are developed in the form of fault trees. The second phase is application. Sensors are installed on the system to provide information about current system performance from which the potential causes can be deduced. A simple system example is used to demonstrate the features of the method. To illustrate the potential for the method to deal with additional system complexity and redundancy, a section from an aircraft fuel system is used. A discussion of the results is provided.     

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.     

New methods to determine the importance measures of initiating and enabling events in fault tree analysis

Components' importance measures play a very important role in system reliability analysis. They are used to identify the weakest parts of the system for design improvement, failure diagnosis and maintenance. This paper deals with the problem of determining the importance measures of basic events in case of unreliability analysis of binary coherent and non-coherent fault trees. This type of analysis is typical of catastrophic top events, characterised by unacceptable consequences. Since the unreliability of systems with repairable components cannot be exactly calculated via fault tree, the Expected Number of Failures - which is obtained by integrating the unconditional failure frequency - is considered as it represents a good upper bound. In these cases it is important to classify events as initiators or enablers since their roles in the system are different, their sequence of occurrence is different and consequently they must be treated differently. New equations based on system failure frequency are described in this paper for determining the exact importance measures of initiating and enabling events. Simple examples are provided to clarify the application of the proposed calculation methods. Compared with the exact methods available in the literature, those proposed in this paper are easier to apply by hand and are simpler to implement in a fault tree analyser.