A logical model for quantification of occupational risk

Functional block diagrams (FBDs) and their equivalent event trees are introduced as logical models in the quantification of occupational risks. Although a FBD is similar to an influence diagram or a belief network it provides a framework for introduction in a compact form of the logic of the model through the partition of the paths of the equivalent event tree. This is achieved by consideration of an overall event which has as outcomes the outmost consequences defining the risk under analysis. This event is decomposed into simpler events the outcome space of which is partitioned into subsets corresponding to the outcomes of the initial joint event. The simpler events can be further decomposed into simpler events creating a hierarchy where the events in a given level (parents) are decomposed to a number of simpler events (children) in the next level of the hierarchy. The partitioning of the outcome space is transferred from level to level through logical relationships corresponding to the logic of the model.Occupational risk is modeled trough a general FBD where the undesirable health consequence is decomposed to “dose” and “dose/response”; “dose” is decomposed to “center event” and “mitigation”; “center event” is decomposed to “initiating event” and “prevention”. This generic FBD can be transformed to activity—specific FBDs which together with their equivalent event trees are used to delineate the various accident sequences that might lead to injury or death consequences.The methodology and the associated algorithms have been computerized in a program with a graphical user interface (GUI) which allows the user to input the functional relationships between parent and children events, corresponding probabilities for events of the lowest level and obtain at the end the quantified corresponding simplified event tree.The methodology is demonstrated with an application to the risk of falling from a mobile ladder. This type of accidents has been analyzed as part of the Workgroup Occupational Risk Model (WORM) project in the Netherlands aiming at the development and quantification of models for a full range of potential risks from accidents in the workspace.     

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。     

Criteria for evaluating protection from single points of failure for partially expanded fault trees

Fault tree analysis (FTA) is a technique that describes the combinations of events in a system which result in an undesirable outcome. FTA is used as a tool to quantitatively assess a system's probability for an undesirable outcome. Time constraints from concept to production in modern engineering often limit the opportunity for a thorough statistical analysis of a system. Furthermore, when undesirable outcomes are considered such as hazard to human(s), it becomes difficult to identify strict statistical targets for what is acceptable. Consequently, when hazard to human(s) is concerned a common design target is to protect the system from single points of failure (SPOF) which means that no failure mode caused by a single event, concern, or error has a critical consequence on the system. Such a design target is common with “by-wire” systems. FTA can be used to verify if a system is protected from SPOF. In this paper, sufficient criteria for evaluating protection from SPOF for partially expanded fault trees are proposed along with proof. The proposed criteria consider potential interactions between the lowest drawn events of a partial fault tree expansion which otherwise easily leads to an overly optimistic analysis of protection from SPOF. The analysis is limited to fault trees that are coherent and static.     

Functional block diagrams and automated construction of event trees

Functional block diagrams are introduced as graphical representations of the function of a system. A functional block provides the output of a system as the outcome of a joint event defined by the inputs to the system and its various states. Functional blocks corresponding to different subsystems are combined together to form a functional block diagram representing the functional characteristics of the combined system. Conversely, a complex system represented by a single functional block is decomposed to constituent components with a corresponding functional block diagram. It is demonstrated that a functional block diagram is an alternative representation of an event-tree corresponding to the outcome space of the underlying joint event. The concept of output space partition is introduced and an algorithm is developed for generating the most compact form of the event-tree consistent with a given partition. This algorithm forms the basis of a technique for the automated construction of an event-tree starting from a developed functional block diagram. This technique is amenable to computerization. Finally, as a demonstration of the technique, the event-trees of a boiling water reactor (BWR) are developed.     

OPTIMUM SIZING OF AIRPORT TERMINAL FACILITIES

This paper reports on the development of an algorithm for computing the minimum amount of space required for an airport terminal. Current practice of computing space requirements relies heavily on “peak-hour” forecasts. These forecasts are suspect because they fail to show the variations which occur within a peak hour, especially now with the use of wide-body jets. To overcome this deficiency an algorithm was devised which takes as input an airline schedule and produces the minimum amount of space required. Since no formal mathematical technique could be found to solve this large combinatorial problem, the algorithm was based on heuristic programming. It allocates loads from flights to facilities in such a manner that the sum of the areas of the facilities is a minimum.     

An ordering heuristic to develop the binary decision diagram based on structural importance

Fault tree analysis is often used to assess risks within industrial systems. The technique is commonly used although there are associated limitations in terms of accuracy and efficiency when dealing with large fault tree structures. The most recent approach to aid the analysis of the fault tree diagram is the Binary Decision Diagram (BDD) methodology. To utilise the technique the fault tree structure needs to be converted into the BDD format. Converting the fault tree requires the basic events of the tree to be placed in an ordering. The ordering of the basic events is critical to the resulting size of the BDD, and ultimately affects the performance and benefits of this technique. A number of heuristic approaches have been developed to produce an optimal ordering permutation for a specific tree. These heuristic approaches do not always yield a minimal BDD structure for all trees. This paper looks at a heuristic that is based on the structural importance measure of each basic event. Comparing the resulting size of the BDD with the smallest generated from a set of six alternative ordering heuristics, this new structural heuristic produced a BDD of smaller or equal dimension on 77% of trials.     

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.     

The interdisciplinary engineering knowledge genome

Parallel to the concept of the human genome and its impact on biology and other disciplines, we revealed a similar concept in engineering sciences, termed the ??Interdisciplinary Engineering Knowledge Genome??, which is an organized collection of system and method ??genes?? that encode instructions for generating new systems and methods in diverse engineering disciplines. Resting on the firm mathematical foundation of combinatorial representations, the Interdisciplinary Engineering Knowledge Genome unifies many engineering disciplines, providing a basis for transforming knowledge between them, supporting new educational practices, promoting inventions, aiding design, and bootstrapping new discoveries in engineering and science. Given the formal underlying combinatorial representations, these merits could be automated. This paper elucidates this new concept and demonstrates its value and power in engineering design.     

Evaluation of seismic performance of an electric substation using event tree/fault tree technique

In this study, we use the event tree/fault tree technique to evaluate the performance of an electric substation in the event of an earthquake. The substation is considered as a combination of components (equipment and structures), and the event trees and fault trees are established to delineate the interrelationships of these components. Using the fragility data of individual components in the event trees and fault trees, the probabilities that the substation as a whole fails at various levels of ground shaking can be determined and displayed as substation fragility curves. Furthermore, using the minimum cut set technique, the most critical and vulnerable component in the substation can be identified. Substation 21, a key electric power supplier to several major hospitals in downtown Memphis, is selected to illustrate this technique.     

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。     

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.     

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.     

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.     

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.     

Using transportation accident databases to investigate ignition and explosion probabilities of flammable spills

Risk assessment of hazardous material spill scenarios, and quantitative risk assessment in particular, make use of event trees to account for the possible outcomes of hazardous releases. Using event trees entails the definition of probabilities of occurrence for events such as spill ignition and blast formation. This study comprises an extensive analysis of ignition and explosion probability data proposed in previous work. Subsequently, the results of the survey of two vast US federal spill databases (HMIRS, by the Department of Transportation, and MINMOD, by the US Coast Guard) are reported and commented on. Some tens of thousands of records of hydrocarbon spills were analysed. The general pattern of statistical ignition and explosion probabilities as a function of the amount and the substance spilled is discussed. Equations are proposed based on statistical data that predict the ignition probability of hydrocarbon spills as a function of the amount and the substance spilled. Explosion probabilities are put forth as well. Two sets of probability data are proposed: it is suggested that figures deduced from HMIRS be used in land transportation risk assessment, and MINMOD results with maritime scenarios assessment. Results are discussed and compared with previous technical literature.     

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.     

基于物元理论的任意功能树相似扩展方法

功能模型是概念设计的核心处理对象,功能树是一种典型的、应用广泛的功能模型。使用现有相似度计算方法计算任意功能树的相似度存在困难。因此,基于布尔代数提出了析取范式树的概念,以及两种求解析取范式树的方法,并描述了任意功能树的物元相似度计算方法。拓展了功能树相似扩展方法的应用范围,扩大了设计解空间,增加了获得创新解的可能性,最后给出实例验证了方法的有效性。     

A stochastic approach to consequence tree analysis

In this paper a stochastic approach to consequence tree analysis is considered. A consequence tree is a set of events logically combined by OR and AND connections that occur in sequence, some being prerequisites for others. Consequence trees are applicable to failure propagation in plants. Facilitating paths and inhibiting cuts are defined and considered. The distribution of the time the system needs to reach a certain top event is obtained. Probability weights are defined that can be used to obtain the weakest link in the consequence tree.