New qualitative analysis strategies in Metaprime

Advanced combinatorial method for solving complex fault trees

Minimal cut sets (or prime implicants: minimal combinations of basic event conditions leading to system failure) are important information for reliability/safety analysis and design. To obtain minimal cut sets for general non-coherent fault trees, including negative basic events or multi-valued basic events, a special procedure such as the consensus rule must be applied to the results obtained by logical operations for coherent fault trees, which will require more steps and time. This paper proposes a simple method for a non-coherent fault tree, whose top event is represented as an AND combination of monotonic sub-trees. A “monotonic” sub-tree means that it does not have both positive and negative representations for each basic event. It is proven that minimal cut sets can be obtained by a conventional method for coherent fault trees. An illustrative example of a simple event tree analysis shows the detail and characteristics of the proposed method.

Since their introduction in form of a canonical representation of logical functions, the Binary Decision Diagrams (BDDs) gained a wide acceptance in numerous industrial applications. This paper summarizes the properties of BDD representation of Minimal Cut Sets (MCS) of Fault Tree (FT) models most typically encountered in nuclear energetics. Cut sets from MCS are defined as paths from the top BDD node to terminal nodes in the BDD, on which a quantitative and qualitative FT analysis (FTA) is performed. The core of the FTA on the BDDs is performed with help of two fundamental algorithms, one for conditional probability evaluation and another for the selection of cut sets. The accuracy of conditional probability evaluation represents an essential feature for an unbiased quantitative analysis, such as the top event probability or the determination of event importance measures. The cut set selection algorithm is shown in a generic version introducing logical predicates for its selection criteria. As it is known, the efficiency of depicted algorithms depends only on the number of BDD nodes used for the FT representation. In order to appraise the compactness of the BDD representation of FT models, their characteristics have herein been evaluated on several real-life models from the Nuclear Power Plant Krško. The extraordinariness of the compactness of the BDD representation reflects in its ability to implement advanced dynamic analysis (i.e. what-if) of FT models. The efficiency of such an approach is recognized by commercial vendors upgrading their FT Tools to new versions by implementing BDD based algorithms.

The subject of research is to determine the functional safety indicators of a fault-tolerant safety-critical system, namely, the minimal cut sets’ probability for a given duration of the system’s operation, using the state transition diagram (STD). The aim is to create a new method for analyzing the functional safety of a fault-tolerant safety-critical system. This method is based on the methodology of developing models of operational reliability behavior in the form of STD. This methodology provides a detailed representation of inoperable states and their relation with pre-failure (inoperable critical) states. The task is to propose a new classification for inoperable states of the STD to obtain all possible emergencies in the same space of inoperable states. This approach allows consideration the correlations between the failures, that it is impossible to use the fault trees. Since the space of inoperable states can reach hundreds and thousands of states, a method is proposed for their automated determination according to the classification. The state space method was used to conduct the validation of the method of functional safety analysis. The following results were obtained: the system of Chapman-Kolmogorov differential equations is formed in accordance with the STD and it provides the dependence of the functional safety indicator – the minimal cut sets’ probability as a function of the operational duration of the fault-tolerant safety-critical system. This dependence is called the emergency function. The method for determining the emergency function is based on the usage of the emergency mask. Note that the proposed model of operational reliability behavior in the form of STD provides the possibility to conduct both the functional safety and the reliability indicators. The value of the minimal cut sets’ probability for a given duration of operation is determined using the fault tree for the validation of the proposed method of functional safety analysis. The fault tree was built by Reliasoft BlockSim software. The obtained value coincides with the value of the minimal cut sets’ probability, which was defined by the emergency function for the same operational duration. Thus, the designer can comprehensively analyze the feasibility of introducing redundancy (structural, temporal, functional). Conclusions: the scientific novelty of the obtained results is the following: the new method for determining safe, critical and catastrophic states in the set of inoperable states is used in the methodology of the STD developing to obtain the stochastic model of operational reliability behavior of fault-tolerant safety-critical system. This technique ensures an automated defining of emergency function by using an improved structural-automatic model.

Fault tree analysis (FTA) is a well-established technique to analyze the safety risks of a system. Two specific prominent FTA methods, largely applied in the aerospace field, are the so-called minimal cut sets (MCS), which uses an approximate evaluation of the problem, and the direct evaluation (DE) of the fault tree, which uses a top-down recursive algorithm. The first approach is only valid for small values of basic event probabilities and has historically yielded faster results than exact solutions for complex fault trees. The second one means exact solutions at a higher computational cost. This article presents several improvements applied to both approaches in order to upgrade the computing performance. First, improvements to the MCS approach have been performed, where the main idea has been to optimize the number of required permutations and to take advantage of the available information from previous solved subsets. Second, improvements to the DE approach have been applied, which deal with a reduction of the number of recursive calls through a deep search for independent events in the fault tree. This could dramatically reduce the computation time for industrial fault trees with a high number of repeated events. Additional implementation improvements have been also applied regarding hash tables, and memory access and usage, but also implementing the so-called “virtual gates”, which enable limitless children on each gate. The results presented hereafter are promising, not only because they show that both approaches have been highly optimized compared to the literature, but also because a DE solution has been achieved, which can compete in time resources (and obviously in precision) with the MCS approach. These improvements are relevant when considering the industrial, and more specifically the aeronautical, implementation and application of both techniques.

International Maritime Organization (IMO) implements the principles of risk management through a systematic process called Formal Safety Assessment (FSA). FSA is a structured and systematic methodology, aimed at enhancing maritime safety, including protection of life, health, the marine environment and property, by using risk analysis and cost benefit assessment. One of the most widely used hazard identification and risk analysis techniques in FSA is Fault Tree Analysis (FTA) method. However, only basic conventional methodology of the FTA technique is used in FSA. When dealing with large fault trees, the limitations of FTA in terms of accuracy and the efficiency become apparent. It is necessary for IMO to improve FTA method in FSA. In recent years, the Binary Decision Diagram (BDD) method has been developed that solves fault trees and overcomes the disadvantages of the conventional FTA approach. In this paper, the BDD method is introduced for the application in FSA, as it has never been used in FSA studies. A commonly used construction method and some basic event ordering methods of BDD are described. By applying BDD to FTA, two main issues concerned in FSA, minimal cut set and top event probability, can be obtained efficiently and accurately comparing to the analysis using a conventional FTA method.

Fussell-Vesely Importance (FVI) is one of the most commonly used importance measures. It is based on the concept of Minimal Cut Sets (MCSs), and it quantifies the contribution of a system component to system failure. In paper (Kvassay et al. 2015), the algorithm for identification of all system MCSs based on Direct Partial Logic Derivatives (DPLDs) has been considered. These MCSs are then used to compute the FVI. However, the FVI of a system component depends only on MCSs that contain the considered component, i.e. it is not necessary to identify all MCSs of the system. This implies that it is useful to develop algorithms that will identify not all system MCSs but only those in which a specific component occurs. Such algorithms can be used to compute the FVI without a priori knowledge of MCSs. In this paper, a new algorithm for this task is proposed. The algorithm is based on a relation between DPLDs and MCSs that is also considered in this paper. of algorithms for identification or generation of MCSs of investigated system. These algorithms are developed mainly on the basis of applied fault trees (Sinnamon & Andrews 1997, Vatn 1992) or networks (Emadi & Afrakhte 2014, Rebaiaia & Ait-Kadi 2013). Another algorithm for identification of system MCSs has been considered in paper (Kvassay et al. 2015). This algorithm is based on tools of logical differential calculus, and it can be used for systems of any type (not only for systems presented as networks or for systems described by fault trees). Logical differential calculus has been developed for analysis of dynamic properties of logic functions. Direct Partial Logic Derivatives (DPLDs) are essential part of this tool (Tapia et al. 1991). Their use in reliability analysis has been considered in several papers (Zaitseva 2003, Zaitseva 2012, Zaitseva et al. 2015). These papers have showed that DPLDs are very appropriate for identification of situations in which failure/repair of a system component results in system failure/repair. This fact has been used to develop algorithms for defining system boundary states and for calculation of some measures that can be used to evaluate system reliability. In this paper, we develop ideas presented in paper (Kvassay et al. 2015) to propose an algorithm that identifies not all system MCSs but only MCSs in which a specified component is presented. Such MCSs are useful in computation of FVI of the considered component. As a result new method for calculation of this IM is developed. This method is

Sand casting operations, though commonplace, pose a significant threat of explosion accidents. This paper presents a novel sand casting safety assessment technique based on fault tree analysis, Heinrich accident triangle, hazard and operability–layer of protection analysis (HAZOP–LOPA) and bow tie model components. Minimal cut sets and minimal path sets are first determined based on fault tree analysis, then the frequency of sand casting explosion accidents is calculated based on the Heinrich accident triangle. Third, the risk level of venting quality can be reduced by adopting HAZOP–LOPA; the residual risk level of venting quality remains excessive even after adopting two independent protective layers. The bow tie model is then adopted to determine the causes and consequences of venting quality. Five preventative measures are imposed to enhance the venting quality of foundry sand accompanied by 16 mitigative safety measures. Our results indicate that the risk attributable to low foundry sand venting quality can be minimized via bow tie analysis.

A new method is developed for tracing the unreliability contributions of system components and recognizing the system weak parts using the fault tree analysis (FTA). The method is based on the minimum cut set (MCS) algorithm for evaluating the system reliability using the FTA and the proportional sharing principle (PSP). The fault tree can be expressed as MCSs and the system unreliability can be mathematically expressed by a certain terms of probability of occurrence of MCSs. A unreliability tracing (UT) principle is proposed for allocating the probability of each term to the basic events fairly and reasonably, and then the direct contribution relationship between the system unreliability and basic events can be established. The system UT sharing factors (UTSFs) are derived to easily identify the weakness parts in a system. The applicability of the proposed methods is illustrated by case studies of a simple system and a multiple-output power distribution system.

In this study, the risk of collision and grounding accidents on bulk carrier and general cargo ships was investigated. A comprehensive risk analysis consisting of past accident reports, fault tree analysis (FTA) and Cut sets importance measure (CS-I) methods was carried out. The failures effective in the occurrence of collision and grounding accidents were determined by examining past accident reports. In the study, the probability for each failure was derived by using real accident data. Using FTA, various potential accident occurrence combinations/scenarios, also known as minimal cut sets (MCSs), for both accident types were obtained. In addition, prioritization was conducted for the MCSs of both types of accidents using CS-I sensitivity analyses. The faults that increase the risk of collision accidents the most were found to be interpretation failure of the Convention on the International Regulations for Preventing Collisions (COLREG) and lack of situational awareness. In addition, the top failures that lead to groundings were determined to be lack of communication in bridge resource management (BRM), fatigue/sleeplessness and inappropriate voyage plan. Recommendations are made for eliminating potential risk factors, preventing the recurrence of such accidents and establishing safer maritime transport.

ABSTRACTThis study aimed to use the fault tree analysis (FTA) to investigate the casual relationship among the event and causes contributing to extremely severe crash that leads to more than 10 deaths. The characteristics of extremely severe traffic crashes were compared with those of normal crashes in terms of gender, driving experience, road technical level, road alignment, time, and weather conditions. A fault tree was developed to provide an overview of the basic causes and their causal relationship. The minimal cut sets were derived to reveal the causal relationships among events and causes contributing to extremely severe crashes. Then, quantitative assessment was conducted to evaluate the importance of various events. The results can help to prioritize actions and resources for crash prevention. Finally, the minimal path set analysis was conducted to identify the minimal sets of basic events needed to be prevented so that extremely severe crash will not occur.

The fault of aerocamera could be caused by many factors, such as flaw of itself, work environment, operation and maintenance. The internal structure of aerocamera is very complex, which is made by many circuit boards. Camera detecting instrument is detectable installation of ground for aerocamera. The detection of aerocamera must be from overall to parts. This paper makes overall scheme design for detecting system of aerocamera. Based on fault tree analysis, this paper comprehensively analyzes the failure mode of exposure board of aerocamera. Minimal cut sets can be got from the fault tree of exposure board. Then the flow of testing can be established by minimal cut sets. Finally, the testing of exposure board is finished.

In order to take advantage of the computer in the numerical calculation, in view of the fault tree qualitative analysis, a new method of fault tree analysis, numerical methods, was proposed on the basis of absorbing merits of the prime number method and determinant method. The fault tree's minimum cut sets and path sets can be calculated effectively with this method. Consequently, a specific example about calculation of the minimum cut sets was demonstrated with Scilab in this paper.

Embedded systems are used everywhere. They are complex systems whose failure may cause death or injury to people or may damage the environment are required to be safety safe. Therefore, these systems need to be analyzed. Fault tree analysis is a common way for performing safety analysis. It generates a large amount of interconnected data that itself needs to be analyzed to help dierent domain experts (e.g., engineers and safety analysts) in their decisions for improving the system’s safety. Additional diculties occur for the experts in communication and in linking the data (e.g., information of basic events or minimal cut sets) to the actual parts of the system (model). Therefore, a large amount of time and eort is being spent on discussions, searching, and navigating through the data. To overcome this, we present a new metaphor called “CakES” consisting of multiple views visualizing the data generated by fault tree analysis and linking them to the actual parts of the model by intuitive interaction. Using the interaction techniques of CakES the user can directly explore the safety related data without navigating through the fault tree while retaining an overview of all critical aspects in the model.

This paper deals with the reliability assessment of electrical power supply systems under redundancy. For doing so, three probabilistic safety analysis (PSA) methods are proposed and developed namely fault tree analysis (FTA), reliability block diagram (RBD), and Monte Carlo Simulation (MC) method. The FTA method is performed using RiskSpectrumPSA® software and the RBD and MC methods are coded using Matlab software. The electrical power supply system reliability is analyzed and enhanced considering various cases of redundancy. The FTA method is based on qualitative and quantitative reliability assessment. The quantitative assessment calculates the failure probability of the top event, and the qualitative approach determines the minimal cut sets (MCS). However, the RBD and MC methods are proposed to compute the system failure probability. The considered methods are applied on three case studies and the obtained results are compared to each other. The obtained results show that the three methods provide almost the same results. Furthermore, the reliability of the electrical power supply is clearly enhanced with the number of redundant components.