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The effectiveness of contemporary strategies for conducting fault tree/event tree (FTET) analyses within the realm of probabilistic risk assessment has recently come under rigorous examination. In light of such investigation, facility managers have gained a more profound understanding of the risk and safety implications inherent in the structural and componential integrity of systems (structures, systems, and components). This comprehensive research endeavor harnesses the power of risk models, employing both FTET and binary decision diagrams, to scrutinize and optimize the operational performance of a 10-MW reference Russian research reactor [Water-Water Research Reactor (VVR)] within the framework of probabilistic safety assessment. Moreover, this investigation delves into the intricate web of interrelationships existing among an array of analytical methodologies. These encompass the Fussell-Vesely (FV) importance measure, criticality analysis, Birnbaum analysis, risk achievement worth (RAW), and the differential importance measure, all with a focus on specific foundational events and vital components. Additionally, this note delves into the analysis of multiple significant measures frequently employed for VVR. Notably, the study establishes that merely two importance measures (IMs) prove sufficient for the core damage equation. Furthermore, this note investigates various important measures often employed for VVR. It is shown that two IMs are enough for the core damage equation. In conclusion, RAW, FV importance, or a blend of the two are adequate enough to be frequently employed for the VVR. [ABSTRACT FROM AUTHOR]

This paper introduces an improved methodology designed to address a practical deficit of existing methodologies by incorporating circuit-level analysis in the assessment of building microgrid reliability. The scientific problem at hand involves devising a systematic approach that integrates circuit modeling, Probability Density Function (PDF) selection, formulation of reliability functions, and Fault Tree Analysis (FTA) tailored specifically for the distinctive features of building microgrids. This method entails analyzing inter-component relationships to gain comprehensive insights into system behavior. By harnessing the circuit models and theoretical framework proposed herein, precise estimations of microgrid failure rates can be attained. To complement this approach, we propose a thorough investigation utilizing reliability curves and importance measures, providing valuable insights into individual device failure probabilities over time. Such time-based analysis plays a crucial role in proactively identifying potential failures and facilitating efficient maintenance planning for microgrid devices. We demonstrate the application of this methodology to the University of Antioquia (UdeA) Microgrid, a low-voltage system comprising critical components such as solar panels, microinverters, inverters/chargers, batteries, and charge controllers. [ABSTRACT FROM AUTHOR]

With the constant progress made in the development of modern industrial technology, more and more highly integrated complex systems have emerged, whose reliability is often enhanced by setting system redundancy. When the reliability analysis is conducted on a complex system with redundancy, however, the failure of the redundancy management function hinders the spare parts from being converted as normal, which is called imperfect coverage (IPC). If the impact of IPC is ignored, the results of reliability analysis would be rendered inaccurate. Therefore, a multi-state Takagi–Sugeno dynamic fault tree (T–S DFT) analysis which considers IPC is proposed in this study to improve the accuracy of reliability analysis for the complex multi-state dynamic system. Firstly, the description rules of multi-state Takagi–Sugeno (T–S) dynamic gates are given. Secondly, the input and output of the warm spare (WSP) gate with IPC are analyzed to calculate the probability density function of the output of the WSP gate which considers IPC. Compared with the classical distribution, phase-type (PH) distribution shows satisfactory generality and analytical characteristics, which makes it suitable for dealing with complex random problems. Therefore, the life distribution of components is assumed to be PH distribution. Furthermore, the importance measures of multi-state T–S DFT analysis are presented. Finally, the reliability and importance measures of a radio station system are calculated to provide reference for identifying weak links, optimizing reliability design and maintaining operation. [ABSTRACT FROM AUTHOR]

This paper introduces an improved methodology designed to address a practical deficit of existing methodologies by incorporating circuit-level analysis in the assessment of building microgrid reliability. The scientific problem at hand involves devising a systematic approach that integrates circuit modeling, Probability Density Function (PDF) selection, formulation of reliability functions, and Fault Tree Analysis (FTA) tailored specifically for the distinctive features of building microgrids. This method entails analyzing inter-component relationships to gain comprehensive insights into system behavior. By harnessing the circuit models and theoretical framework proposed herein, precise estimations of microgrid failure rates can be attained. To complement this approach, we propose a thorough investigation utilizing reliability curves and importance measures, providing valuable insights into individual device failure probabilities over time. Such time-based analysis plays a crucial role in proactively identifying potential failures and facilitating efficient maintenance planning for microgrid devices. We demonstrate the application of this methodology to the University of Antioquia (UdeA) Microgrid, a low-voltage system comprising critical components such as solar panels, microinverters, inverters/chargers, batteries, and charge controllers.

Systems are damaged due to various disturbances, and the reliability of the systems is reduced. Measures to improve system resilience need to be studied since many systems still need to operate normally after suffering damage. In this paper, the whole process of the disturbance and recovery of the system is considered, and a resilience optimization model of a multi-component system is proposed. Firstly, a system resilience assessment method is proposed based on system reliability, and the system resilience loss is used as the resilience assessment index. Secondly, two component importance indexes, loss importance and recovery importance, are proposed for the system disturbance phase and recovery phase, respectively. The two importance indexes are weighted to obtain the weighted importance so as to measure the change law of system resilience and determine the influence degrees of components on system reliability. Then, under the constraint of maintenance time, an optimization model is established to determine a redundancy strategy to maximize system resilience. Finally, through an example analysis of a wind turbine system with its main components, it is verified that the redundancy strategy proposed with this method can reduce the loss of system resilience and effectively improve system reliability. [ABSTRACT FROM AUTHOR]

The crew of a nuclear‐powered submarine under development in Brasil plays an important role in its safety. For this reason, crew members must be trained in procedures against undesired events. However, information that would help to accurately decrease human error probability (HEP) on board nuclear‐powered submarines is not available in the literature. Therefore, a methodology is required to obtain this information. This study introduces importance measures to evaluate the contribution of performance shaping factors (PSFs) and their levels to HEP. Importance measures Fussell‐Vesely, risk reduction worth, risk achievement worth, and Birnbaum importance, commonly used in probabilistic safety assessment, are introduced to identify PSFs and PSF levels that contribute the most to HEP. The proposed approach is focused on identifying HEP's main contributors, oriented toward decision‐making. The methodology uses the PSFs established in the Standardized Plant Analysis Risk‐Human Reliability Analysis method and a Bayesian network to quantify HEP. Moreover, the results of an application case demonstrate the method's effectiveness in integrating expert opinions into representative values of HEP and in identifying critical PSFs and PSF levels that should be the object of the decision‐making process to improve human performance. [ABSTRACT FROM AUTHOR]

Investments in mini hydropower plants (MHPP) in Serbia are associated with numerous risks, both in the construction and exploitation phases. To assess these risks, this study proposes a methodology combining fault tree analysis and risk matrix using data obtained through a survey and semi-structured interviews with domain experts. Conducting qualitative fault tree analysis, 21 events have been identified that may jeopardize the success of the mini hydropower plant project finance. Based on expert assessments of probability of these events and their financial, reputational, and environmental impacts, risk matrix results showed that public protests, lack of projects sponsors' capital, and problems related to hydrology can be considered as events with the highest risk. In addition, quantitative analysis has been conducted to obtain the priority of measures for risk elimination or reduction. The quantitative fault tree analysis and three importance measures have indicated that measures must first be taken to prevent public protests during the implementation and exploitation phases, and a risk of watercourse abuse in the MHPP project. [ABSTRACT FROM AUTHOR]

Systems are damaged due to various disturbances, and the reliability of the systems is reduced. Measures to improve system resilience need to be studied since many systems still need to operate normally after suffering damage. In this paper, the whole process of the disturbance and recovery of the system is considered, and a resilience optimization model of a multi-component system is proposed. Firstly, a system resilience assessment method is proposed based on system reliability, and the system resilience loss is used as the resilience assessment index. Secondly, two component importance indexes, loss importance and recovery importance, are proposed for the system disturbance phase and recovery phase, respectively. The two importance indexes are weighted to obtain the weighted importance so as to measure the change law of system resilience and determine the influence degrees of components on system reliability. Then, under the constraint of maintenance time, an optimization model is established to determine a redundancy strategy to maximize system resilience. Finally, through an example analysis of a wind turbine system with its main components, it is verified that the redundancy strategy proposed with this method can reduce the loss of system resilience and effectively improve system reliability.

Over the years, probabilistic nature of renewable energy sources (RES) and its influence on power system adequacy have been well studied. However, rather less attention has been paid to the impact of RES unit itself's and its power conversion system's (PCS') reliability, as well as their various connection topologies. This paper devises a comprehensive sensitivity study on how each of these elements can affect overall generating system reliability. given the plethora of RES configurations and components, it is of import to identify the most vulnerable element in RES. In this work, component importance is extended, for the first time, to generating capacity adequacy assessment (HLI). Measurement index is the centerpiece in reliability importance. New indices have to be introduced to facilitate the study. While the physical meaning of previously developed indices is lost, in this study indices are proposed based on traditional importance measures, of which the physical meaning are strictly retained and consistent with the definitions. With the proposed assessment technique, components in various RES configuration can be ranked according to their reliability importance. It is found in the numerical study that different importance measures (such as risk-achievement based measures and risk-reduction based measures) can result in different rankings. Studies on contributing factors of the reliability importance are also performed. As more and more RES gaining foothold in generating systems, the proposed technique assist to achieve targeted reliability level of the system, by easily identifying and prioritizing reliability improvement tasks among various units/components in the increasing complex system.

In risk analysis, sensitivity measures quantify the extent to which the probability distribution of a model output is affected by changes (stresses) in individual random input factors. For input factors that are statistically dependent, we argue that a stress on one input should also precipitate stresses in other input factors. We introduce a novel sensitivity measure, termed cascade sensitivity, defined as a derivative of a risk measure applied on the output, in the direction of an input factor. The derivative is taken after suitably transforming the random vector of inputs, thus explicitly capturing the direct impact of the stressed input factor, as well as indirect effects via other inputs. Furthermore, alternative representations of the cascade sensitivity measure are derived, allowing us to address practical issues, such as incomplete specification of the model and high computational costs. The applicability of the methodology is illustrated through the analysis of a commercially used insurance risk model. [ABSTRACT FROM AUTHOR]

The availability of ageing systems, particularly weapon systems within the Department of Defense, is of significant concern, as budgets tighten and system replacement is infeasible. This work addresses the selection of sole suppliers according to their ability to provide component parts that strengthen availability of the system. We extend a popular multi-criteria decision-making approach, Technique for Order Preferences by Similarity to an Ideal Solution, by (i) considering the availability of individual components as the criteria in the decision problem and (ii) weighting those criteria according to the value of component importance measures while (iii) accounting for uncertainty in underlying reliability and maintainability parameters with interval numbers. An aircraft example illustrates the approach. [ABSTRACT FROM AUTHOR]

This paper introduces a novel feature selection method, called Feature Selection based on Importance Measures (FS-IM), to enhance the forecasting of crude oil returns. FS-IM innovatively combines active learning with the application of Gaussian noise to input features and selects the most relevant features using an optimal threshold value. The paper applies a ridge regression (RR) model based on FS-IM (FS-RR) to identify the factors that have important information for crude oil return forecasting. The paper compares FS-IM with other dimension reduction methods such as Principal Component Analysis (PCA), Kernel Principal Component Analysis (KPCA), and Independent Component Analysis (ICA). The results show that FS-IM can significantly improve model accuracy, demonstrating its effectiveness in finding key features. Moreover, FS-IM is more stable and consistent than other dimension reduction methods in enhancing the prediction accuracy in different scenarios, indicating its superior capability in capturing complex relationships between input and output variables. Furthermore, this study compares FS-RR model with other 13 prediction models by conducting experiments using a series of evaluation metrics, different statistical tests, and different step-ahead predictions and training sets. The results confirm that the RR model based on FS-IM can consistently outperform other model in terms of predictive performance and economic value, proving its effectiveness and robustness. This study contributes to the literature on crude oil price forecasting by addressing the challenges of high-dimensional and complex data, and by providing a robust, practical tool for professionals in energy economics and finance. • A new feature selection method for crude oil forecasting using importance scores and Gaussian noise is proposed. • The method selects the most relevant features based on the prediction errors of a base forecasting model. • The method enhances the accuracy and value of ridge regression model compared to other methods. • The method handles high-dimensional and complex data without losing information or interpretability. [ABSTRACT FROM AUTHOR]

System reliability/availability is a complex concept that is evaluated based on numerous indices and measures. There are different methods for the calculation of these indices and measures in reliability analysis. Some of the most used indices are important measures. These measures allow us to evaluate the influence of fixed system components or set of components to the system reliability/availability. Importance measures are used today to allow for various aspects of the impact of system elements on its failure or operability. Analysis of element importance is used in the system design, diagnosis, and optimization. In this paper new algorithms for the calculation, some of the important measures are developed based on the matrix procedures. This paper's goal is the development of a new algorithm to calculate importance measures of the system based on the matrix procedures that can be transformed in the parallel procedures/algorithms. These algorithms are developed based on the application of Logical Differential Calculus of Boolean logic for the important analysis of the system. The application of parallel algorithms in importance analysis allows the evaluation of the system of large dimensions. Importance specific of the proposed matrix procedures for calculation of importance measures is the application of structure-function for the mathematical representation of the investigated system. This function defined the correlation of the system components states and system reliability/ availability. The structure-function, in this case, is defined as a truth vector to be used in the matrix transformation. The truth vector of a Boolean function is a column of the truth table of function if the values of the variables are lexicographically ordered. Therefore, the structure-function of any system can be represented by the truth vector of 2n elements un-ambiguously.

This paper presents a probabilistic failure analysis of leakage of the oil and gas in a subsea production system using fault tree analysis (FTA). A fault tree was constructed by considering four major areas where the leakages can be initiated. These are: gas and oil wells, pipelines, key facilities and third party damage. Conventional FTA requires precise values for the probability of failure of the basic events. However, since the failure data are uncertain, a fuzzy approach to these data is taken which leads to the so-called fuzzy fault tree analysis (FFTA), a method that employs expert elicitation and fuzzy set theories to calculate the failure probabilities of the intermediate events and the top event through identification of the minimal cut sets of the fault tree. A number of importance measures for minimal cut sets and the basic events have been obtained which helps to identify the nature of dependence of the top event on the basic events and thereby can identify the weakest links that may cause leakage in the subsea production system.

The paper shows the connections between some importance indices for the components in an engineering coherent system and the performance of the system obtained when a redundancy mechanism is applied to a specific component. A copula approach is used to model the dependency among the components. This approach includes the popular case of independent components. Under some assumptions, it is proved that if component i is more important than component j, then the system obtained by applying a redundancy procedure to the ith component is better, under different stochastic criteria, than that obtained with the jth component. These results can be applied to several redundancy mechanisms. A new importance index is defined to study active redundancies. Some illustrative examples are provided. [ABSTRACT FROM AUTHOR]

Summary: The resilience of critical infrastructures has become a major concern throughout the design, operation, and maintenance process in recent years. While traditional evaluation measures are mainly concerned with complete and timely restoration, this work considers simultaneously the cases where systems fail to recover thoroughly or timely. We define resilient limit and propose a new resilience evaluation framework for systems suffering different levels of breakdowns. Furthermore, from perspectives of topological structure, cold standby, and resilient limit of components, this paper proposes three resilience‐based importance measures, namely, structure importance, redundancy importance, and reinforcement importance. Finally, we demonstrate our method with a numerical example, illustrating its effectiveness as a tool to evaluate the influences of component resilience characteristics on the overall system. [ABSTRACT FROM AUTHOR]

Countries around the world suffer the dramatic impact of earthquakes and other natural hazards reflected in casualties, infrastructure damage, service interruptions, and recovery costs. Although disaster exposure consciousness of electric power systems has increased in recent years, mitigation and adaptation actions, such as reserve scheduling and infrastructure investments, are usually performed without quantitative tools to account for the underlying stochasticity of these events. This article first discusses why an integrated assessment, which incorporates sources of uncertainty (risk) and manages the time-dependency of the recovery process (resilience), should be used to assess the impact of seismic events on electric power systems. Thereafter, a probabilistic methodology that considers the hazard, vulnerability, operation, and recovery of the system is presented. As a case study, the probabilistic seismic resilience of the electric power system of Northern Chile is assessed using different risk measures, including expected annual loss, value at risk, and conditional value-at-risk. Finally, a novel criticality assessment based on these metrics is developed to demonstrate that, for certain networks such as the study case, retrofit of selective components can notably improve the resilience of the complete system to seismic events. For example, if one specific component from the 152 components of the study system is assumed invulnerable, expected annual interruption costs decrease by 8%. [ABSTRACT FROM AUTHOR]

Probabilistic risk assessment (PRA) is used as an essential tool for risk-informed decision-making in the nuclear industry. The fault and event trees play a crucial role in PRA to estimate the probability of system failure based on the failure probabilities of components. The fault trees or event trees for an actual power plant unit can be fairly large in size with several different types of logic gates, interconnected events, dependent events, etc. A large fault tree can include hundreds of gates, basic events (BEs), multiple occurring events (MOEs), and dependent events. Complex connectivities can give rise to excessive computational demand and storage requirements for the analysis. Fault and event trees can be solved using the minimal cut-set approaches, or advanced quantification techniques such as Binary decision diagrams or Bayesian networks. However, these techniques can be computationally inefficient for larger fault trees and can run out of memory/storage space. This study focuses on developing and proposing a new approach for accurate estimation of the system-level risk while improving the computational efficiency significantly. More specifically, an attempt is made to reduce the complexity of the analysis of MOEs and dependent events in fault trees. The proposed algorithms in this study present a significant improvement over traditional approaches which makes it highly promising for additional development. The computational efficiency of the proposed approach over the traditional approach is illustrated for fault trees with a varying number of events and different types of logic gate connections. • Limitations of traditional PRA tools. • Exact quantification of risk for event and fault tree analysis. • Computationally efficient PRA tool based on compressed truth tables. • Importance measure calculation without minimal cut sets. [ABSTRACT FROM AUTHOR]

• Study an importance-based generalized system cost model for different phases in life cycle. • Discuss operation and maintenance costs due to the different types of component failures. • Give a specific selection method for performing end-of-life in case of component failure. • Propose improvement importance to optimize system reliability under invariant resources. • Analyze failure risk under limited and unlimited resource using improvement importance. System life cycle can be divided into four phases: the production phase, the operation phase, maintenance phase and the end-of-life phase. Component failure leads to the different variable costs in different phases. Existing studies have investigated systems from a cost-effectiveness perspective of the operation and maintenance stage, which may not be holistic. Furthermore, the expected failure cost can be used to evaluate the failure risk. In this paper, a generalized system cost for different phases is analyzed in life cycle, then a risk optimization is studied based on an improvement importance. Firstly, a comprehensive life cycle cost model is proposed. Specifically, the operation and maintenance costs due to the different types of component failures are discussed, respectively. Besides, a specific selection method for performing end-of-life in case of component failure is given using the recovery importance. Secondly, an improvement importance is proposed to optimize system reliability under invariant resources. Thirdly, the specific process of the failure risk under limited resource using improvement importance is analyzed. Finally, the proposed methods are verified using two applications, and a discussion on unlimited resources for risk optimization is given. [ABSTRACT FROM AUTHOR]

One of the purposes of system reliability analysis is to identify the weaknesses or the critical components in a system and to quantify the impact of component’s failures. Various importance measures are being introduced by many researchers since 1969. These component importance measures provide a numerical rank to determine which components are more important to system reliability improvement or more critical to system failure. In this paper, we overview various components importance measures and briefly discuss them with examples. We also discuss some other extended importance measures and review the developments in study of various importance measures with respect to some of the popular reliability systems.

Importance measures are integral parts of risk assessment for risk‐informed decision making. Because the parameters of a risk model, such as the component failure rates, are functions of time and a perturbation (change) in their values can occur during the mission time, time dependence must be considered in the evaluation of the importance measures. In this paper, it is shown that the change in system performance at time t, and consequently the importance of the parameters at time t, depends on the parameters perturbation time and their value functions during the system mission time. We consider a nonhomogeneous continuous time Markov model of a series‐parallel system to propose the mathematical proofs and simulations, while the ideas are also shown to be consistent with general models having nonexponential failure rates. Two new measures of importance and a simulation scheme for their computation are introduced to account for the effect of perturbation time and time‐varying parameters. [ABSTRACT FROM AUTHOR]

• Improvement of the single-loop estimation of the moment independent importance measures. • Proposed procedure based on Importance Sampling. • Applications on some numerical test cases. Moment independent importance measures have been proposed by Borgonovo [1] in order to alleviate some of the drawbacks of variance-based sensibility indices. They have gained increasing attention over the last years but their estimation remains a challenging issue. An effective estimation scheme in the case of correlated inputs, referred to as single-loop method, has been proposed by Wei et al. [2]. In this paper we show via simulation that this method may be inaccurate, making for instance 40% error in the simplest possible Gaussian case. We then propose a new estimation scheme which greatly improves the accuracy of the single-loop method, up to a factor 10 in some simple numerical examples. We prove that our estimator is strongly consistent and several simulation results are presented to demonstrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Resilience of systems to failures during functioning is of great practical importance. One of the strategies that might be considered to enhance reliability and resilience of a system is swapping components when a component fails, thus replacing it by another component from the system that is still functioning. This paper studies this scenario, particularly with the use of the survival signature to quantify system reliability, where it is assumed that such a swap of components requires these components to be of the same type. We examine the effect of swapping components on a reliability importance measure for the specific components, and we also consider the joint reliability importance of two components. Such swapping of components may be an attractive means toward more resilient systems and could be an alternative to adding more components to achieve redundancy of repair and replacement activities. [ABSTRACT FROM AUTHOR]

Abstract With the development of offshore wind power, the reliability analysis of offshore wind turbines is increasingly significant due to the system complexity and negative impacts in harsh operating conditions. In this study, the Fault Tree Analysis method is adopted for both qualitative and quantitative evaluation of semi-submersible floating offshore wind turbine failure characteristics. The floating offshore wind turbine is divided into several assemblies, including support structures, pitch and hydraulic system, gearbox, generator and the other systems. Failure rates of relevant offshore structures are collected from previous studies, reports and reliability databases. On this basis, the quantitative assessment of Minimum Cut Sets and Importance Measures are achieved. The calculated results are generally in conformity with statistical data, indicating that most of the failures are caused by several basic factors. Marine conditions, especially the salt-spray and high wind speed, show the most significant impact on floating offshore wind turbine performance. Highlights • Fault Tree Analysis method is proposed for evaluation of floating offshore wind turbine failure. • The floating offshore wind turbine is divided into several assemblies. • Failure rates of relevant offshore structures are collected from previous studies. • Quantitative assessment of Minimum Cut Sets and Importance Measures are achieved. • Salt-spray and high wind speed, show the most significant impact on wind turbine performance. [ABSTRACT FROM AUTHOR]

In probabilistic risk assessment, attention is often focused on the expected value of a risk metric. The sensitivity of this expectation to changes in the parameters of the distribution characterizing uncertainty in the inputs becomes of interest. Approaches based on differentiation encounter limitations when (i) distributional parameters are expressed in different units or (ii) the analyst wishes to transfer sensitivity insights from individual parameters to parameter groups, when alternating between different levels of a probabilistic safety assessment model. Moreover, the analyst may also wish to examine the effect of assuming independence among inputs. This work proposes an approach based on the differential importance measure, which solves these issues. Estimation aspects are discussed in detail, in particular the problem of obtaining all sensitivity measures from a single Monte Carlo sample, thus avoiding potentially costly model runs. The approach is illustrated through an analytical example, highlighting how it can be used to assess the impact of removing the independence assumption. An application to the probabilistic risk assessment model of the Advanced Test Reactor large loss of coolant accident sequence concludes the work. [ABSTRACT FROM AUTHOR]

Abstract: Risk analysts are often concerned with identifying key safety drivers, that is, the systems, structures, and components (SSCs) that matter the most to safety. SSCs importance is assessed both in the design phase (i.e., before a system is built) and in the implementation phase (i.e., when the system has been built) using the same importance measures. However, in a design phase, it would be necessary to appreciate whether the failure/success of a given SSC can cause the overall decision to change from accept to reject (decision significance). This work addresses the search for the conditions under which SSCs that are safety significant are also decision significant. To address this issue, the work proposes the notion of a θ‐importance measure. We study in detail the relationships among risk importance measures to determine which properties guarantee that the ranking of SSCs does not change before and after the decision is made. An application to a probabilistic safety assessment model developed at NASA illustrates the risk management implications of our work. [ABSTRACT FROM AUTHOR]

In the structural reliability analysis, there exist multiple failure modes. Influence of each failure mode on the structural system reliability needs to be considered, because it is significant for simplifying the system model and improving the performance of the system. By using the concepts of the importance measures(IM) in probability risk assessment (PRA), the importance indices in PRA are extended to measure the failure mode contribution to the structural system reliability, and the analytical solutions of the failure mode importance measure for the parallel and series structural systems are derived firstly. Then, copula method is proposed to estimate the importance indices for the nested hybrid structural systems. At last, one numerical example with a parallel structure and two engineering examples are employed to analyze the failure mode importance and to test the two estimates based on the analytical solution and the copula method. Result indicates that five PRA importance indices can well reflect the failure mode importance. It also shows that the copula method is highly suitable for computing PRA IMs in the intricate structural systems. [ABSTRACT FROM AUTHOR]

Importance measures (IMs) are used for risk-informed decision making in system operations, safety, and maintenance. Traditionally, they are computed within fault tree (FT) analysis. Although FT analysis is a powerful tool to study the reliability and structural characteristics of systems, Bayesian networks (BNs) have shown explicit advantages in modeling and analytical capabilities. In this paper, the traditional definitions of IMs are extended to BNs in order to have more capability in terms of system risk modeling and analysis. Implementation results on a case study illustrate the capability of finding the most important components in a system. [ABSTRACT FROM AUTHOR]

This paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous components. The particular cases of independent components and homogeneous components are also considered. We model the dependence structure among the components by the concept of copula. The proposed measure allows us to provide the best estimation of the system lifetime, in terms of the mean squared error, under the assumption that the lifetime of one of its components is known. We include theoretical results that are useful to calculate a closed-form of our measure and to compare two components of a system. We also provide some procedures to approximate the importance measure by Monte Carlo simulation methods. Finally, we illustrate the main results with several examples. [ABSTRACT FROM AUTHOR]

The wind energy industry is expanding in order to be able to meet the current and future energy demand, and is supported by governments in that renewable energy investment has been made. Optimal decision making (DM) in wind turbine manufacturing is required to guarantee the competitiveness of the business. This paper considers decision making for wind turbine manufacturing using a logical decision tree (LDT) and binary decision diagrams (BDD). A qualitative analysis of wind turbine manufacturing is carried out using logical decision trees. They are used for a qualitative study of the case study. Binary decision diagrams are used to obtain the Boolean function and, therefore, to carry out a quantitative analysis. Finally, an optimization of budgets is employed based on importance measures. There is no optimal method that can establish the importance measures. The following heuristic methods have been used to find a solution close to the optimal: Fussell-Vesely, Birnbaum and Criticality. The computational cost is reduced by ranking the events. The heuristic methods to establish the best rankings are: Top-Down-Left-Right, Level based method, AND based method, Breadth-First Search (BFS) and Depth First Search (DFS). A real case study is considered, in which a static and dynamic analysis is carried out.

Risk-informed decision making is often accompanied by the specification of an acceptable level of risk. Such target level is compared against the value of a risk metric, usually computed through a probabilistic safety assessment model, to decide about the acceptability of a given design, the launch of a space mission, etc. Importance measures complement the decision process with information about the risk/safety significance of events. However, importance measures do not tell us whether the occurrence of an event can change the overarching decision. By linking value of information and importance measures for probabilistic risk assessment models, this work obtains a value-of-information-based importance measure that brings together the risk metric, risk importance measures, and the risk threshold in one expression. The new importance measure does not impose additional computational burden because it can be calculated from our knowledge of the risk achievement and risk reduction worth, and complements the insights delivered by these importance measures. Several properties are discussed, including the joint decision worth of basic event groups. The application to the large loss of coolant accident sequence of the Advanced Test Reactor helps us in illustrating the risk analysis insights. [ABSTRACT FROM AUTHOR]

The topological importance or functional importance is only taken into consideration, when the existing measures are constructed. Based on functional properties of components, generalized importance measures, which improve topological measures in network theory, are proposed to combine with Choquet integral. In order to overcome the uncertainty and randomness, which exist if a single importance measure identifies critical components, aggregation operator (AO) is given through fusion multi-generalized importance measures and then used to identify critical components of complex electromechanical system. Finally, a case study which selects fuzzy integral to treat as AO is presented to identify critical components of bogie system. The results show that the method with Choquet integral regarding as AO and k fuzzy measure calculating weights, is effective. [ABSTRACT FROM AUTHOR]

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The Birnbaum importance measure plays a central role in reliability analysis. It has initially been introduced for coherent systems, where several of its properties hold and where its computation is straightforward. This work introduces a Boolean expression for the notion of criticality that allows the seamless extension of the Birnbaum importance to non-coherent systems. As a key feature, the novel definition makes the computation and encoding straightforward with well-established techniques such as Binary Decision Diagrams (BDDs) or Fault Trees (FTs). Several examples and a case study illustrate the findings. [ABSTRACT FROM AUTHOR]