Traditional Importance Measures Research Articles

Marginal and joint failure importance for K-terminal network edges under counting process

Importance measures have been applied extensively in various fields such as reliability optimization, failure diagnosis, and risk analysis. Traditional importance measures are insufficient for networks because they only quantify the contribution of each edge's reliability to network reliability. The counting process is a kind of stochastic process that can count the number of edge failures appeared in a time of period, which requires less information than knowing all edge reliabilities. In the context of edge failures subject to a counting process, this paper investigates importance measures for a given binary K-terminal network including n binary edges. This paper develops some formulas to compute the joint failure importance (JFI) and the marginal failure importance (MFI). The MFI quantifies the changes of network failure probability caused by the change of edge state, while the JFI evaluates the interaction effect between two edges regarding network failure probability. Their values, as functions of time t, depend on the probability distribution of the total number of edge failures at time t and the network structure. Additionally, we present a Monte-Carlo algorithm to approximate the values of the MFI and JFI. Finally, a numerical example concerning the road network is provided to demonstrate the computation methods of MFI and JFI, whose edge failures are subject to a saturated nonhomogeneous Poisson process. The numerical results provide further insights for the road network regarding the importance of edges.

Risk-based bridge component importance measures under seismic loads

This article formulates risk-based component importance measures (RCIMs) to identify critical components for a bridge subjected to earthquakes. RCIM, unlike traditional reliability-based importance measures, is well suited for complex systems like bridges as it uses a flexible system failure definition using bridge level risk consequences or performance objectives. Contrasting traditional notions of risk and reliability related to structural system failures, the RCIMs embrace a broader definition of risk which includes consequences of system failure to society and the environment. System failure is defined as exceedance of a user-defined threshold of system risk (e.g. based on cost, emissions, embodied energy, or other metrics). Our definition of system failure using global performance metrics helps relating component to system reliability explicitly and offers an alternative perspective to aggregate joint failure events of bridge components into relevant damage states. RCIM combines information about the reliability of a component and its contribution to the system performance and hence the importance measures developed offer risk mitigation indicators for decision makers as to which components may require upgrade to achieve a given performance objective. The proposed RCIMs generalize existing importance measures through analytical exploration of the entire space of system configurations with correlated component failures, while also considering multiple risk-based criteria beyond reliability. These RCIMs, demonstrated through a seismic bridge system case study, further show that as the bridge components age and the hazard intensity varies, the relative contribution of the components to system risk also shifts.

Reliability Importance of Renewable Energy Sources to Overall Generating Systems

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.

System Reliability Allocation and Optimization Based on Generalized Birnbaum Importance Measure

Importance measure can be used to identify the most vulnerable components with respect to system functionality or failure. Traditional importance measures may not be effective to evaluate the contribution of an individual component if its reliability value does not fall in the full range between 0 and 1. Based on the cost–reliability relation, this paper proposes a generalized Birnbaum importance measure (GBIM) to quantify the contribution of individual components to system reliability improvement by considering reliability range, manufacturing complexity, and technology feasibility. Since GBIM possesses several unique features in terms of guiding system reliability optimization, in this paper, we further develop a GBIM-based genetic algorithm to solve a type of optimal reliability allocation problem. The numerical studies show that both the computational efficiency and the near global optimality based on GBIM outperforms the methods using the traditional importance measures.

Reliability Importance Measures for Network Based on Failure Counting Process

Traditional importance measures seldom consider how the number of failed components influences the network reliability. This paper proposes two importance measures under the circumstance that the failure sequence of the components follows a counting process. The first importance measure aims to assess the contribution of the individual component (edge) to the network failure. The second evaluates the contribution of the individual component to the network functionality. Both importance measures are time-dependent functions, and their values are jointly determined by the network structure and the distribution of the number of failed components at a particular time. We prove that the proposed importance measures are able to generate consistent rankings based on edge's impact on the network reliability behavior. When networks possess special structure or the number of failed edges follows the special distribution, the rankings are coincident with the results generated from some traditional importance measures. When component's failure sequence follows a saturated nonhomogeneous Poisson process, the proposed importance measures are equivalent to the structural importance measure as time approaches zero or infinite. Finally, numerical examples are provided to demonstrate the application and performance of the proposed measures.

A cost-based integrated importance measure of system components for preventive maintenance

Preventive maintenance may be performed on a few selected components when a component fails. Importance measures can be used to identify the most important component that requires maintenance. However, this process involves two problems: (a) the preventive maintenance time of the selected component may be bigger than the maintenance time of the failed component; (b) the most important component may incur the highest maintenance cost. Traditional importance measures do not consider the possible effect of maintenance time and cost, which significantly affect the improvement of system reliability. Given the joint effect of component maintenance cost and time on system reliability, this study proposes a cost-based integrated importance measure (IIM) to identify the component or group of components that may be selected for preventive maintenance. The characteristics of cost-based IIM are examined to determine the relationships among failure rates, shape parameters, and the scale parameters of different components. Finally, an application to a wind turbine system is used to illustrate its usage.

Analyzing sensitivity measures using moment-matching technique

Sensitivity indices are used to rank the importance of input design variables or components by estimating the degree of uncertainty of output variable influenced by the uncertainty generated from input variables or components. With the advent of highly complex engineering simulation models that describe the relationship between input variables and output response, the need for an efficient and effective sensitivity analysis is more demanding. Traditional importance measures either requires extensive random number generations or unable to measure variables interaction effects. In this article, a generalized approach that can provide efficient and accurate global sensitivity indices is developed. The approach consists of two steps; running an orthogonal array based experiment using moment-matched levels of the input variables followed by a variance contribution analysis. The benefits of the approach are demonstrated through different real life examples.

Uncertainty Importance Measure of Individual Components in Multi-State Systems

Traditional reliability importance measures have been successfully extended from binary-state models to multi-state models. The calculation of these measures typically relies on the true reliabilities of components. In reality, however, the true values of component reliabilities are usually unknown, and they are generally approximated by their estimates generated from testing or field failure data. The accuracy of the estimates is limited by the available data. Research on uncertainty importance measures (UIMs) has emerged on this account to rank components based on their potentials to reduce the uncertainty about the estimated system reliability. The UIMs of components for binary-state models are well studied, but there is a lack of studies dedicated to multi-state models. In this paper, the reliability estimator and the corresponding uncertainty (characterized by the variance estimator) are derived for multi-state systems with structures such as serial, parallel, bridge, and their more complex combinations. The derivation process utilizes multinomial reliability testing and the universal generating function method. With the help of the derived estimators, we extend uncertainty importance research to multi-state models through a newly defined variance-based measure. Examples are provided to demonstrate the proposed ideas.

Evaluation of risk impact of changes to Completion Times addressing model and parameter uncertainties

This paper presents an approach and an example of application for the evaluation of risk impact of changes to Completion Times within the License Basis of a Nuclear Power Plant based on the use of the Probabilistic Risk Assessment addressing identification, treatment and analysis of uncertainties in an integrated manner. It allows full development of a three tired approach (Tier 1–3) following the principles of the risk-informed decision-making accounting for uncertainties as proposed by many regulators. Completion Time is the maximum outage time a safety related equipment is allowed to be down, e.g. for corrective maintenance, which is established within the Limiting Conditions for Operation included into Technical Specifications for operation of a Nuclear Power Plant. The case study focuses on a Completion Time change of the Accumulators System of a Nuclear Power Plant using a level 1 PRA. It focuses on several sources of model and parameter uncertainties. The results obtained show the risk impact of the proposed CT change including both types of epistemic uncertainties is small as compared with current safety goals of concern to Tier 1. However, what concerns to Tier 2 and 3, the results obtained show how the use of some traditional and uncertainty importance measures helps in identifying high risky configurations that should be avoided in NPP technical specifications no matter the duration of CT (Tier 2), and other configurations that could take part of a configuration risk management program (Tier 3).

On the Use of the Importance Measure for Multi-State Repairable k-out-of-n: G Systems

Importance measures in reliability systems are used to identify weak components in contributing to proper functioning of the system. Traditional importance measures mainly concern the change of the system reliability as the change of the reliability of one component and seldom consider the expected number of repairs of the objective component in unit time. This paper proposes an improvement potential rate importance (IPR) to verify the effectiveness of the improvement in system reliability for multi-state repairable k-out-of-n: G systems. Then the comparisons between IPR and Birnbaum importance are discussed. Finally, a case study is given to demonstrate the proposed IPR.

Importance Analysis Method of Fuzzy Fault Tree Based on T-S Modle and Application in Hydraulic System

In order to overcome the shortage of dealing with fuzzy information and uncertainty of fault logical relationship in traditional importance measures, the fuzzy set theory is presented to fault tree, using fuzzy number to describe the fault states of system and components, and using fuzzy subsets to denote the fault rates, a fuzzy fault tree of T-S modle was established. And a model of fuzzy fault tree was established and a T-S fuzzy importance analysis method was presented on the basis of T-S analysis method. The method is applied in the importance analysis of hydraulic system, and proving that the algorithms are feasible.

Integrated importance measure for multi-state coherent systems of k level

To verify the effectiveness of the integrated importance measure (IIM) for multi-state coherent systems of k level,the definition and physical meaning of IIM are demonstrated.Then,the improvement potential and Δ-importance measures are generalized to multi-state coherent systems based on the system performance level,and the relationships between IIM and traditional importance measures are discussed.The characteristics of IIM are demonstrated in both series and parallel systems.Also,an application to an oil transportation system is given.The comparison results show that: (i) IIM has some useful properties that are not possessed by traditional importance measures; (ii) IIM is effective in evaluating the component role in multi-state systems when the component reliability and the failure rate are simultaneously considered.

Importance Measure Method for Ranking the Aircraft Component Vulnerability

A relevant outcome of aircraft vulnerability assessment is the identification of the vulnerability importance of components for survivability design. However, when comparing the contribution of the components to the whole aircraft vulnerability, there is no accepted criterion regarding the component vulnerability. This work is aimed at investigating how importance measures in the field of reliability can be accounted for in the ranking of vulnerable components. The traditional importance measures (e.g., Birnbaum, Fussell–Vesely, criticality, reliability achievement worth, and reliability reduction worth) are modified to rank the component vulnerability. Three examples of increasing complexity are provided. Analysis shows that the traditional single-hit vulnerable area criterion is a special case among the proposed importance measures, and it can only apply for the nonredundant aircraft model with no component overlap; the importance measures can be applied to rank the component vulnerability of a complex aircraft (i.e., redundant aircraft model with component overlap). Another important aspect different from reliability analysis is that, in an overlap region, the change of the vulnerability of one component will probably lead to the change of the vulnerability of the shielded components, and in the process of computing the vulnerability importance measure metrics, this chain reaction should be considered.

Risk importance measures in the dynamic flowgraph methodology

This paper presents new risk importance measures applicable to a dynamic reliability analysis approach with multi-state components. Dynamic reliability analysis methods are needed because traditional methods, such as fault tree analysis, can describe system's dynamical behaviour only in limited manner. Dynamic flowgraph methodology (DFM) is an approach used for analysing systems with time dependencies and feedback loops. The aim of DFM is to identify root causes of a top event, usually representing the system's failure. Components of DFM models are analysed at discrete time points and they can have multiple states. Traditional risk importance measures developed for static and binary logic are not applicable to DFM as such. Some importance measures have previously been developed for DFM but their ability to describe how components contribute to the top event is fairly limited. The paper formulates dynamic risk importance measures that measure the importances of states of components and take the time-aspect of DFM into account in a logical way that supports the interpretation of results. Dynamic risk importance measures are developed as generalisations of the Fussell-Vesely importance and the risk increase factor.

A modified variance-based importance measure and its solution by state dependent parameter

To overcome the disadvantage of traditional variance-based importance measures, i.e. the effects of different realizations of input variables on output response may mutually counteract each other, a modified variance-based importance measure is presented for importance analysis of the input variables. The proposed measure analyses the importance of the input variables comprehensively in terms of the expectation and variance of the output response. Compared with the traditional variance-based importance analysis method, the modified importance measure indices not only reflect the old one, but also provide a very useful supplement for it. Furthermore, combined with the advantages of the state dependent parameter model, a solution to the proposed measure indices is provided. Several examples are introduced to show that the modified importance measure is more comprehensive and reasonable, and the solution based on the state dependent parameter method can improve computational efficiency considerably with acceptable precision.

Moment-independent importance measure of basic variable and its state dependent parameter solution

To analyze the effect of basic variable on output of the structure or system in reliability engineering, two moment-independent importance measures of the basic variable are proposed respectively on the failure probability and distribution function of the output. The importance measures proposed not only inherit the advantages of the traditional moment-independent importance measures, but also reflect the intrinsic relationship of the moment-independent measures and the corresponding variance-based importance measures. For the problem that the computational effort of the moment-independent importance measure is usually too high, the computation of the proposed moment-independent importance measures is transformed into that of the variance-based importance measures on their intrinsic relationship. And then combining the high efficient state dependent parameter (SDP) method for the calculation of the conditional moments of the model output, a SDP solution is established to solve two moment-independent importance measures. Several examples are used to demonstrate that the proposed importance measures can effectively describe the effect of the basic variable on the reliability of the structure system, and the established solution can obtain the two importance measures simultaneously with only a single set of model runs, which allows for a strong reduction of the computational cost.

Integrated importance measures of multi-state systems under uncertainty

Importance analysis in reliability engineering is used to find the weakest components in a system. Traditional importance measures for multi-state systems analysis mainly pay attention to the reliability or structure characteristics of components, but seldom consider the causalities between components in the system under uncertainty. In order to solve the above problems, the multi-state system Bayesian network is proposed to represent the multi-state system under uncertainty and facilitate the component importance calculation. Then, this paper puts forward a separate subset algorithm based on the Bayesian information criterion and K2 algorithm to build the multi-state system Bayesian network of practical systems automatically. By considering the reliability, structure and causality characteristics of components comprehensively, the integrated importance measure is also presented to describe the effects of component failures on the state distribution of the multi-state system under uncertainty. Finally, the application of the multi-state system Bayesian network, the separate subset algorithm and the integrated importance measure in a simple head-up display system is implemented to verify the effectiveness of the proposed methods in components importance analysis.

On the use of uncertainty importance measures in reliability and risk analysis

This paper discusses the use of uncertainty importance measures in reliability and risk analysis. Such measures are used to rank the importance of components (activities) of complex systems. The measures reflect to what degree the uncertainties on the component level influence the uncertainties on the system level. An example of such a measure is the change in the variance of the reliability of the system when ignoring the uncertainties in the component reliability. The measures are traditionally based on a Bayesian perspective as knowledge-based (subjective) probabilities express the epistemic uncertainties about the reliability and risk parameters introduced. In this paper we carry out a rethinking of the rationale for such measures. What information do they provide compared to the traditional importance measures such as the improvement potential and the Birnbaum measure? To discuss these issues we distinguish between two situations: (A) the key quantities of interest are observable quantities such as the occurrence of a system failure and the number of failures and (B) the key quantities of interest are fictional parameters constructed to reflect the aleatory uncertainties. A new type of combined sets of measures are introduced based on an integration of a traditional measure and a related uncertainty importance measure. A simple reliability example is used to illustrate the analysis and findings.

Joint importance of multistate systems

Importance measures in reliability engineering are used to identify weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system. Traditional importance measures for multistate systems mainly concern reliability importance of an individual component and seldom consider the utility performance of the systems. This paper extends the joint importance concepts of two components from the binary system case to the multistate system case. A joint structural importance and a joint reliability importance are defined on the basis of the performance utility of the system. The joint structural importance measures the relationship of two components when the reliabilities of components are not available. The joint reliability importance is inferred when the reliabilities of the components are given. The properties of the importance measures are also investigated. A case study for an offshore electrical power generation system is given.

Importance measures for nuclear waste repositories

Several importance measures are identified for possible use in the performance assessment of a high-level nuclear waste repository. These importance measures are based on concepts of importance used in system reliability analysis, but the concepts are modified and adapted to the special characteristics of the repository and similar passive systems. In particular, the importance measures proposed here are based on risk (in comparison to traditional importance measures which are based on frequency of failure) and are intended to be more suitable to systems comprised of components whose behavior is most easily and naturally represented as continuous, rather than binary. These importance measures appear to be able to evaluate systems comprised of both continuous-behavior and binary-behavior components. Three separate examples are provided to illustrate the concepts and behavior of these importance measures. The first example demonstrates various formulations for the importance measures and their implementation for a simple radiation safety system comprised of a radiation source and three shields. The second example demonstrates use of these importance measures for a system comprised of components modeled with binary behavior and components modeled with continuous behavior. The third example investigates the use of these importance measures for a proposed repository system, using a total system model and code currently under development. Currently, these concepts and formulations of importance are undergoing further evaluation for a repository system to determine to what degree they provide useful insights and to determine which formulations are most useful.