Component Importance Measures Research Articles

Measures of Inland Waterway Network Resilience

AbstractInland waterways represent a vital component in the larger multi‐modal transportation network that maintains commodity flows across the US. These waterways are subject to disruptive events including whether malevolent attacks, natural disasters, manmade accidents, or common failures. As such, an ability to quantify the vulnerability and recoverability of inland waterways, as it pertains to the inclusive measure of network resilience, is addressed in this work. The paper deploys existing resilience measures to quantify the resilience of inland waterway networks, including: (i) a stochastic measure of time required for the network to achieve full resilience, and (ii) associated resilience‐based component importance measures that highlight the critical waterway links that contribute to waterway network resilience. A data‐driven case study illustrates these metrics to describe commodity flows along the various links of the US Mississippi River Navigation System.

Components Importance Analysis Fault Tree of Power Transformer of Gi Simangkuk Switchyard in Indonesia

The purpose of this paper is to study the importance measures of power transformer system components. Importance measures analysis is a key part of the system reliability quantification process which are most effective towards safety improvement. This paper presented an application and results of the importance measures analysis of a power transformer system of GI Simangkuk switchyard in Indonesia by using Birnbaum importace measures, critically importance measure, and Fussel-Vessely importance measures. These method present the rank of the component importance measures quantitavily according to their contribution to system reliability and safety.

Component importance for linear consecutive‐ k ‐Out‐of‐ n and m ‐Consecutive‐ k ‐Out‐of‐ n systems with exchangeable components

AbstractMeasuring the relative importance of components in a mechanical system is useful for various purposes. In this article, we study Birnbaum and Barlow‐Proschan importance measures for two frequently studied system designs: linear consecutive k ‐out‐of‐ n and m ‐consecutive‐ k ‐out‐of‐ n systems. We obtain explicit expressions for the component importance measures for systems consisting of exchangeable components. We illustrate the results for a system whose components have a Lomax type lifetime distribution. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Resilience-based network component importance measures

Disruptive events, whether malevolent attacks, natural disasters, manmade accidents, or common failures, can have significant widespread impacts when they lead to the failure of network components and ultimately the larger network itself. An important consideration in the behavior of a network following disruptive events is its resilience, or the ability of the network to “bounce back” to a desired performance state. Building on the extensive reliability engineering literature on measuring component importance, or the extent to which individual network components contribute to network reliability, this paper provides two resilience-based component importance measures. The two measures quantify the (i) potential adverse impact on system resilience from a disruption affecting link i, and (ii) potential positive impact on system resilience when link i cannot be disrupted, respectively. The resilience-based component importance measures, and an algorithm to perform stochastic ordering of network components due to the uncertain nature of network disruptions, are illustrated with a 20 node, 30 link network example.

Relationship and Changing Analysis of Birnbaum Importance for Different Components with Bayesian Networks

Importance measures are widely used in reliability engineering. To support system reliability optimization, this paper studies the relationship and changing characteristics of the Birnbaum importance measures (BMs) for different components in binary coherent systems. First, the probabilistic meaning of BM and a modeling method for binary coherent system based on Bayesian network (BN) are presented. Then, the relationship of BMs for different components is explored according to the position of corresponding nodes (components) in BN structures. Later, the changing of BMs for different components, which is caused by the reliability improvements of related root or middle nodes (components) in BN structures, is analyzed respectively. Finally, an illustrative example of a helicopter convertor is implemented to demonstrate the calculation and application process of the relationship and changing characteristics in binary coherent systems with BN. The experimental analysis results substantiate the correctness and effectiveness of the proposed relationship and changing characteristics of BMs for different components.

Hierarchical Modeling by Recursive Unsupervised Spectral Clustering and Network Extended Importance Measures to Analyze the Reliability Characteristics of Complex Network Systems

The complexity of large-scale network systems made of a large number of nonlinearly interconnected components is a restrictive facet for their modeling and analysis. In this paper, we propose a framework of hierarchical modeling of a complex network system, based on a recursive unsupervised spectral clustering method. The hierarchical model serves the purpose of facilitating the management of complexity in the analysis of real-world critical infrastructures. We exemplify this by referring to the reliability analysis of the 380 kV Italian Power Transmission Network (IPTN). In this work of analysis, the classical component Importance Measures (IMs) of reliability theory have been extended to render them compatible and applicable to a complex distributed network system. By utilizing these extended IMs, the reliability properties of the IPTN system can be evaluated in the framework of the hierarchical system model, with the aim of providing risk managers with information on the risk/safety significance of system structures and components.

Extended Component Importance Measures Considering Aleatory and Epistemic Uncertainties

We introduce extended component importance measures (Birnbaum importance, RAW, RRW, and Criticality importance) considering aleatory and epistemic uncertainties. The Dempster-Shafer theory, which is considered to be a less restricted extension of probability theory, is proposed as a framework for taking into account both aleatory and epistemic uncertainties. The epistemic uncertainty defined in this paper is the total lack of knowledge of the component state. The objective is to translate this epistemic uncertainty to the epistemic uncertainty of system state, and to the epistemic uncertainty of importance measures of components. Affine arithmetic allows us to provide much tighter bounds in the computing process of interval bounds of importance measures, avoiding the error explosion problem. The efficiency of the proposed measures is demonstrated using a bridge system with different types of reliability data (aleatory uncertainty, epistemic uncertainty, and experts' judgments). The influence of the epistemic uncertainty on the components' rankings is described. Finally, a case study of a fire-detector system located in a production room is provided. A comparison between the proposed measures and the probabilistic importance measures using two-stage Monte Carlo simulations is also made.

A cost-based importance measure for system components: An extension of the Birnbaum importance

In reliability engineering, component importance measures are used to prioritise components in a system for purposes such as reliability improvement and maintenance planning. Existing importance measures have paid little attention to the costs incurred by maintaining a system and its components within a given time period. Cost-effectiveness analysis, however, is critically important in increasingly competitive markets. This paper proposes a new cost-based importance measure which considers costs incurred by maintaining a system and its components within a finite time horizon. Possible extensions are discussed and examples are given to show the use of the new measure.

Assessment of Seismic Risk and Importance Measures of Interdependent Networks using a Non Simulation-Based Method

Infrastructure networks are critical backbones of urban society that support virtually every economic and societal activity. Recent events have shown that these systems are susceptible to natural and man-made hazards such as earthquakes, hurricanes, and terrorist attacks, and have the potential risk of creating cascading failures due to their interdependent nature. Therefore, analyzing the vulnerability of these complex interacting infrastructures under potential hazards is critical for the development of risk mitigation strategies and effective response and recovery. To assess the seismic risk on the infrastructure, non simulation-based methods have the merit of rapid risk assessment for infrastructures and the associated decision making, because they are efficient in estimating sensitivities and conditional probabilities which are often used for identifying critical components. This article presents a non simulation-based method to assess the system reliability of complex interdependent infrastructure networks under seismic hazards. Also proposed are methods to compute importance measures to gauge the relative contribution of components to system reliability. A case study is presented to demonstrate the proposed approach that can efficiently estimate the reliability of a network system, the effect of interactions between two networks, and the importance measures of components.

Innovative approaches for addressing old challenges in component importance measures

Importance measures (IM) are component related indices that allow assessing how a component in a system affects one or more system level performance functions. While several IM have been presented in the literature, challenges still remain with respect to the following: (1) multiple ranking—multiple perspective, (2) multi-component importance and, (3) multi-function importance. To address these challenges, this paper proposes set of innovative solutions based on several available techniques: Hasse diagram, Copeland score and Multi-objective optimization. As such, the purpose of this research is twofold: first propose solutions and second foster new research to address these challenges. Each of the proposed solutions is exemplified with a working example.

Some Recent Advances on Importance Measures in Reliability

Many importance measures have been proposed with respect to the diverse considerations of system performance, reflecting different probabilistic interpretations and potential applications. This paper studies importance measures in reliability, including their definitions, probabilistic interpretations, properties, computations, and comparability. It categorizes importance measures into the structure, reliability, and lifetime types based on the knowledge for determining them. It covers importance measures of individual components, and ones of pairs and groups of components. It also investigates importance measures in consecutive-k-out-of-n systems.

최소절단집합과 최소경로집합을 이용한 구조 및 신뢰성 중요도 척도의 개발 및 적용

The research discusses interrelationship of structural and reliability importance measures which used in the probabilistic safety assessment. The most frequently used component importance measures, such as Birnbaum`s Importance (BI), Risk Reduction (RR), Risk Reduction Worth (RRW), RA (Risk Achievement), Risk Achievement Worth (RAW), Fussel Vesely (FV) and Critically Importance (CI) can be derived from two structure importance measures that are developed based on the size and the number of Minimal Path Set (MPS) and Minimal Cut Set (MCS). In order to show an effectiveness of importance measures which is developed in this paper, the three representative functional structures, such as series-parallel, k out of n and bridge are used to compare with Birnbaum`s Importance measure. In addition, the study presents the implementation examples of Total Productive Maintenance (TPM) metrics and alternating renewal process models with exponential distribution to calculate the availability and unavailability of component facility for improving system performances. System state structure functions in terms of component states can be converted into the system availability (unavailability) functions by substituting the component reliabilities (unavailabilities) for the component states. The applicable examples are presented in order to help the understanding of practitioners.

Component Reliability Criticality or Importance Measures for Systems With Degrading Components

This paper proposes two new importance measures: one new importance measure for systems with -independent degrading components, and another one for systems with -correlated degrading components. Importance measures in previous research are inadequate for systems with degrading components because they are only applicable to steady-state cases and problems with discrete states without considering the continuously changing status of the degrading components. Our new importance measures are proposed as functions of time that can provide timely feedback on the critical components prior to failure based on the measured or observed degradation. Furthermore, the correlation between components is considered for developing these importance measures through a multivariate distribution. To evaluate the criticality of components, we analysed reliability models for multi-component systems with degrading components, which can also be utilized for studying maintenance models. Numerical examples show that the proposed importance measures can be used as an effective tool to assess component criticality for systems with degrading components.

COMBINATORIAL APPROACH TO COMPUTING COMPONENT IMPORTANCE INDEXES IN COHERENT SYSTEMS

We consider binary coherent systems with independent binary components having equal failure probability q. The system DOWN probability is expressed via its signature's combinatorial analogue, the so-called D-spectrum. Using the definition of the Birnbaum importance measure (BIM), we introduce for each component a new combinatorial parameter, so-called BIM-spectrum, and develop a simple formula expressing component BIM via the component BIM-spectrum. Further extension of this approach allows obtaining a combinatorial representation for the joint reliability importance (JRI) of two components. To estimate component BIMs and JRIs, there is no need to know the analytic formula for system reliability. We demonstrate how our method works using the Monte Carlo approach. We present several examples of estimating component importance measures in a network when the DOWN state is defined as the loss of terminal connectivity.

Measures of component importance in repairable multistate systems—a numerical study

Dynamic and stationary measures of importance of a component in a repairable multistate system are an important part of reliability. For multistate systems little has been published until now on such measures even in the nonrepairable case. According to the Barlow–Proschan type measures a component is important if there is a high probability that a change in the component state causes a change in whether or not the system state is above a given state. On the other hand, the Natvig type measures focus on how a change in the component state affects the expected system uptime and downtime relative to the given system state. In the present paper we first review these measures which can be estimated using advanced simulation methods. Extending earlier work from the binary to the multistate case, a numerical study of these measures is then given for two three component systems, a bridge system and also applied to an offshore oil and gas production system. In the multistate case the importance of a component is calculated separately for each component state. Thus it may happen that a component is very important at one state, and less important, or even irrelevant at another. Unified measures combining the importances for all component states can be obtained by adding up the importance measures for each individual state. According to these unified measures a component can be important relative to a given system state but not to another. It can be seen that if the distributions of the total component times spent in the non-complete failure states for the multistate system and the component lifetimes for the binary system are identical, the Barlow–Proschan measure to the lowest system state simply reduces to the binary version of the measure. The extended Natvig measure, however, does not have this property. This indicates that the latter measure captures more information about the system.

Importance measures in risk-informed decision making: Ranking, optimisation and configuration control

This paper describes roles, extensions and applications of importance measures of components and configurations for making risk-informed decisions relevant to system operations, maintenance and safety. Basic importance measures and their relationships are described for independent and mutually exclusive events and for groups of events associated with common cause failures. The roles of importances are described mainly in two groups of activities: (a) ranking safety significance of systems, structures, components and human actions for preventive safety assurance activities, and (b) making decisions about permissible permanent and temporary configurations and allowed configuration times for regulation, technical specifications and for on-line risk monitoring. Criticality importance and sums of criticalities turn out to be appropriate measures for ranking and optimization. Several advantages are pointed out and consistent ranking of pipe segments for in-service inspection is provided as an example. Risk increase factor and its generalization risk gain are most appropriately used to assess corrective priorities and acceptability of a situation when components are already failed or when planning to take one or more components out of service for maintenance. Precise definitions are introduced for multi-failure configurations and it is shown how they can be assessed under uncertainties, in particular when common cause failures or success states may be involved. A general weighted average method is compared to other candidate methods in benchmark cases. It is the preferable method for prediction when a momentary configuration is known or only partially known. Potential applications and optimization of allowed outage times are described. The results show how to generalize and apply various importance measures to ranking and optimization and how to manage configurations in uncertain multi-failure situations.

Post-hazard flow capacity of bridge transportation network considering structural deterioration of bridges

The flow capacity of a transportation network can be reduced significantly if its constituent bridges are damaged by natural or man-made hazards. For rapid risk-informed decision making on hazard mitigation and response, it is therefore essential to have a capability to predict the post-hazard flow capacity of the network efficiently and accurately. However, this is a challenging task due to the uncertainty in hazards and structural damage, and the complex nature of the network flow analysis. Moreover, the bridge structures may experience significant deterioration over their life cycle, which requires time-varying network reliability analysis. This paper proposes a new non-sampling-based approach to estimate the time-varying post-hazard flow capacity of a bridge transportation network considering structural deterioration of bridges. The proposed approach evaluates the probabilities of structural damage scenarios efficiently using the matrix-based system reliability method and rapidly computes the corresponding flow capacities using a maximum flow capacity analysis algorithm. The matrix-based framework facilitates the integration of these results to obtain the probabilistic distributions and statistical moments of the network flow capacity. It also enables computing various measures useful for risk-informed decision making, such as the conditional mean and standard deviation of flow capacity given observed structural damage, and component importance measures. In the proposed approach, probability calculation and network flow analysis are performed separately, which renders time-varying post-hazard flow capacity analysis efficient. The proposed approach is demonstrated by a numerical example based on the Sioux Falls network under multiple bridge-deterioration scenarios simulating the progress of deterioration.

Seismic Reliability Assessment of Bridges with User-Defined System Failure Events

Bridge-level failure event definitions per limit state have evolved from failure of one key bridge component as representative of the whole bridge system to failure of at least one of multiple components. However, an entire set of bridge failure event possibilities exists between these two extremes in the same limit state, such as failure of any two, any three, or any desired subset of bridge components. This paper proposes a closed-form combinatorial method to evaluate all possible ways in which bridge components can fail within and across limit states. It also highlights bridge component importance measures as key by-products of the closed-form solution. Calculations are illustrated with a particular yet illustrative system failure event, called the augmented event, which incorporates failures of at least one component in a given limit state and joint failures of multiple important components in a previous limit state. Bridges in as-built and retrofitted conditions are used to illustrate the augmentation calculation under seismic loads and the application of the proposed system reliability method. The results reveal an increase in median system fragility at the moderate limit states in the range of 4–20% relative to traditional approaches that neglect augmentation. This methodology to connect bridge components to bridge system reliability can readily support infrastructure stakeholder decision making and risk management through an efficient approach that can adapt to evolving system failure event definitions.

A Component Importance Measure Suitable for Flow Transmission Multi-state Systems

A Component Importance Measure Suitable for Flow Transmission Multi-state Systems

Improved particle swarm optimization to minimize periodic preventive maintenance cost for series-parallel systems

This study minimizes the periodic preventive maintenance cost for a series-parallel system using an improved particle swam optimization (IPSO). The optimal maintenance periods for all components in the system are determined efficiently. Though having advantages such as simple understanding and easy operation, a typical particle swam optimization (PSO) is easily trapped in local solutions when optimizing complex problems and yields inferior solutions. The proposed IPSO considers maintainable properties of a series-parallel system. The importance measure of components is utilized to evaluate the effects of components on system reliability when maintaining a component. Accordingly, the important components form superior initial particles. Furthermore, an adjustment mechanism is developed to deal with the problem in which particles move into an infeasible area. A replacement mechanism is implemented that replaces the first n particles ranked in descending order of total maintenance cost with randomly generated particles in the feasible area. The purpose of doing so is overcome the weakness in that a typical PSO is easily trapped in local solutions when optimizing a complex problem. An elitist strategy is also applied within the IPSO. Additionally, this study employs response surface methodology (RSM) via systematic parameters experiments to determine the optimal settings of IPSO parameters. Finally, a case demonstrates the effectiveness of the proposed IPSO in optimizing the periodic preventive maintenance model for series-parallel systems.