Probability-based extensive quantitative risk analysis: collision and grounding case studies for bulk carrier and general cargo ships

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.

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.

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.

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.

In the process of ship collision avoidance, the occurrence of human errors and its probability are stochastic and fuzzy. It is difficult to use the traditional Fault Tree Analysis method to carry out the quantitative analysis. To solve the problem, the fuzzy fault tree of ship collision from human errors was established by using fuzzy numbers to represent the occurrence probability of basic events and top event. And the grey relational analysis method was applied to the qualitative and quantitative analysis of fuzzy fault tree. The fuzzy significance set of the basic events was taken as a reference sequence, while the characteristic matrix made up of minimal cut sets was taken as a comparative sequence. The failure mode of human factor which may greatly influence the occurrence of ship collision was obtained by calculating the relational degrees between the fault mode of human factor represented by the minimal cut set and ship collision accident, which provides a reference for decision making to reduce the impact of human errors on ship collision accident..

Wind turbines are complex and expensive equipment, requiring high reliability and low maintenance costs. However, most of the existing fault tree analysis (FTA) methods for reliability analysis of wind turbines assume that the repair of wind turbines can restore them to as good as new condition, which is called perfect repair. This assumption may not be realistic in practice, as the repair may not fully recover the original performance or functionality of the equipment or may introduce new defects or errors. This phenomenon is called imperfect repair, which can reduce the reliability of wind turbines over time. To consider the imperfect repair effect in reliability analysis, we present a new FTA approach in this study. In order to predict and assess the failure intensity and dependability of wind turbines under imperfect repair, the proposed FTA technique uses a log-linear proportional intensity model (LPIM). Failure probability, failure rate, and mean time to failure can all be improved with the suggested FTA technique for wind turbines operating with poor repair. The proposed FTA method can also identify the critical components or failure modes most affected by the imperfect repair effect and suggest preventive maintenance actions to improve the reliability of wind turbines. We demonstrate the applicability and effectiveness of the proposed FTA method through a case study on a real or hypothetical wind turbine system under imperfect repair. The findings indicate that the proposed FTA method offers a more precise and authentic assessment of the reliability of wind turbines in the presence of imperfect repair, in contrast to existing FTA methods that assume perfect repair. The findings also demonstrate that the electrical system, hydraulic system, gearbox, generator, and blade are the most critical components or failure modes affecting the system's reliability.

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.

FPSOs have a risk profile different from fixed platforms and commercial trading tankers. Being stationed in one location and routinely visited by supply boats and shuttle tankers. FPSOs can be collided by these ships. In addition, passing ships also pose a collision risk if an FPSO is close to a sailing route. This paper presents a systematic approach to address the risk of collision and contact damage. It is aimed to propose a framework that can be applied in structural designs and risk assessment schemes. The focus is placed on accident scenarios, evaluation approaches and acceptance criteria, the three major issues for a risk assessment and also for a relevant design standard. Accident scenarios and the associated occurrence frequency may be determined through statistics from historical data, expert opinions, and risk analysis, depending on different situations. A spectrum of tools has been developed in recent years that predicts the structural damage of collisions, including simple formulae, simplified analytical methods, simplified FEM, and non-linear FEM simulations. Those based on the advanced structural crashworthiness theory provide powerful and practical tools, and are well suited for design evaluations and risk analysis. Contact damage is more likely to occur than accidents resulting in rupture of shell plating. However, this type of accident has received very limited attention. An analytical approach is presented for analyzing contact damage that can be used during earlier design stage. Acceptance criteria for collision and contact accidents are discussed. The emphasis is on structural integrity including local strength and hull performance. Introduction FPSOs have a risk profile different from fixed platforms and commercial trading tankers. Being stationed in one location and routinely visited by supply boats and shuttle tankers. FPSOs can be collided by these ships. In addition, passing ships also pose a collision risk if an FPSO is close to a sailing route. A collision accident can lead to costly consequences in loss of lives, damage to property and/or environment. As past accidents have demonstrated, the indirect cost of compensation and bad publicity can be even higher. This has been the driving force in recent years for developing standards for design against collision accidents for trading oil tankers. A collision with low kinetic energy can result in permanent deformations of side structures instead of rupture of side shell. This low-energy collision is sometimes called "contact accident". Usually, contact damage is not catastrophic and does not pose a threat to the safety of the installation and the protection of environment. Contact damage receives little attention. This paper presents a systematic approach to address the risk of collision and contact damage. It proposes a framework that can be applied in structural design and risk assessment. Discussion is given to accident scenarios and acceptance criteria.

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

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.

A railway substation transforms the electric power transmitted from electric power plants and supplies it to the railway power system for the appropriate operation of traction system.For the appropriate operation of the traction system, it is very important to maintain the security of electric power system.This paper proposes the case when an AC railway substation does not operate right, and Fault Tree(FT), Event Tree(ET) and Minimal Cut Sets(MCS) algorithm to calculate the reliability indices of railway substation.Event tree is created and gate results of fault tree analysis are used as the source of event tree probabilities.Fault tree represents the interaction of failures and basic events within a system.Minimal Cut Sets analysis is used to minimize system errors, Event Tree and Fault Tree analysis result is helpful to assessing the reliability to interpreted.The reliability indices can be used to determine the equipment to be replaced for the entire system reliability improvement.

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.

This paper proposes a Fault Tree Analysis (FTA) method for control program (CP) for space systems. Once a serious fault occurs in CP, a space system is lost. To avoid such situation, methods that can clarify its causes and propose its countermeasure are required. The concepts of proposed FTA methods are followings: preparing Fault Tree (FT) templates corresponding to primitive statements in CP, defining FTA procedure, and defining CP rewrite method that makes it easier to conduct FTA. The proposed method is helpful to conduct FTA. As a result of applying the proposed FTA method to the fault that a spinning satellite rotates too fast, we confirm that the proposed method can clarify the causes of the fault.

Objective To investigate IMRT planning process using the combined application of failure modes and effects analysis (FMEA) and fault tree analysis (FTA) by reference to the report of Task Group 100 of the AAPM, and stablish and optimize the quality. Methods A multidisciplinary team detailed the process mapping of IMRT planning using Eclipse TPS. The team evaluated the potential failure modes (FMs) of every process step. The evaluation was divided into two groups according to whether quality management (QM) was considered. For every FM, occurrence (O), severity (S) and detectability (D) by consensus were evaluated, and the product of O, S and D yielded the risk priority number (RPN), which permitted the ranking of the FMs. Finally, FTA was used to determine the root factors contributing to the riskiest failure modes. Results The IMRT plan process consisted of 10 major sub-processes and 33 steps, which amounted to 47 failure modes. For the group without quality management, the RPN of FMs was between 13.2-271.8, 27 of which had RPN≥80, and 18 FMs had S≥8. For the group with quality management, the RPN of FMs was between 11.2-158.4, 11 of which had RPN≥80. The difference of RPN between the two groups was statistically significant (RPN of the group without QM=101.17±66.34, RPN of the group with QM=59.54±35.64, t=8.501, P<0.05). Finally, FTA was used to determine the root factors contributing to the FMs, i. e., prescription dose definition and importing images. Conclusions The FMEA and FTA methods are operable and practical, which can systematically and comprehensively analyze the potential failures and risks existing in the process of IMRT plan. And the FMEA and FTA can contribute to establish and optimize the quality management program in radiotherapy. Key words: Intensity modulated radiotherapy; Failure modes and effects analysis; Failure tree analysis; Quality management

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.