COMBINATORIAL APPROACH TO COMPUTING COMPONENT IMPORTANCE INDEXES IN COHERENT SYSTEMS

2011 ◽  
Vol 26 (1) ◽  
pp. 117-128 ◽  
Author(s):  
Ilya B. Gertsbakh ◽  
Yoseph Shpungin
Keyword(s):  
System Reliability ◽  
Simple Formula ◽  
Analytic Formula ◽  
Importance Measure ◽  
Coherent Systems ◽  
Joint Reliability ◽  
Component Importance ◽  
Definition Of ◽  
Combinatorial Parameter ◽  
Combinatorial Representation

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.

scholarly journals Component importance in coherent systems with exchangeable components

2015 ◽  
Vol 52 (3) ◽  
pp. 851-863 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Importance Measure ◽  
Coherent System ◽  
Coherent Systems ◽  
System A ◽  
Component Importance

This paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results.

Representations of component importance for coherent systems with exchangeable components

2020 ◽  
Vol 57 (2) ◽  
pp. 385-406
Author(s):  
S. Pitzen ◽  
M. Burkschat
Keyword(s):  
Order Statistics ◽  
Distribution Functions ◽  
Importance Measure ◽  
Coherent Systems ◽  
Sequential Order ◽  
Limiting Behavior ◽  
Sequential Order Statistics ◽  
Component Importance ◽  
Dependent Component ◽  
Two Measures

AbstractTwo definitions of Birnbaum’s importance measure for coherent systems are studied in the case of exchangeable components. Representations of these measures in terms of distribution functions of the ordered component lifetimes are given. As an example, coherent systems with failure-dependent component lifetimes based on the notion of sequential order statistics are considered. Furthermore, it is shown that the two measures are ordered in the case of associated component lifetimes. Finally, the limiting behavior of the measures with respect to time is examined.

scholarly journals Computational method for importance measure of the k-out-of-n system based on stress–strength interference

2019 ◽  
Vol 234 (1) ◽  
pp. 27-40
Author(s):  
Dong Lyu ◽  
Shubin Si ◽  
Zhiqiang Cai ◽  
Liyang Xie
Keyword(s):  
System Reliability ◽  
Strength Distribution ◽  
Computational Method ◽  
Risk Assessments ◽  
System Level ◽  
Importance Measure ◽  
Relative Significance ◽  
Numerical Examples ◽  
Component Importance ◽  
Distribution Parameters

Importance measures, which are used to evaluate the relative significance of various components to system reliability, have been widely applied in system reliability designs and risk assessments. This article deals with the importance measure for the k-out-of- n system of which components are loaded by common stress. Based on system-level stress–strength interference model, a new computational method for the Birnbaum importance measure is proposed for the k-out-of- n system. Then, two numerical examples are presented to further illustrate the proposed method and some key contents are discussed particularly as follows: (1) the importance measures for the system with s-identical components and nonidentical components are developed, (2) component importance changes as its own strength distribution parameters change and (3) the new method corrects the errors caused by ignoring the failure dependency.

Reliability and Importance Measures for Combined m-Consecutive-k-Out-of-n: F and Consecutive-kb-Out-of-n: F Systems with Non-Homogeneous Markov-Dependent Components

2018 ◽  
Vol 25 (05) ◽  
pp. 1850022 ◽  
Author(s):  
Mahmoud Boushaba ◽  
Azzedine Benyahia
Keyword(s):  
Closed Form ◽  
Generating Function ◽  
System Reliability ◽  
Probability Generating Function ◽  
Importance Measure ◽  
Joint Reliability ◽  
Independent Case ◽  
New Formula ◽  
Marginal Reliability ◽  
F System

A Combined [Formula: see text]-Consecutive-[Formula: see text]-out-of-[Formula: see text] and Consecutive-[Formula: see text]-out-of-[Formula: see text]: F System consists of [Formula: see text] components ordered in a line such that the system fails iff there exist at least [Formula: see text] consecutive failed components, or at least [Formula: see text] nonoverlapping runs of [Formula: see text] consecutive failed components, where [Formula: see text]. This system was been introduced by Mohan et al. [P. Mohan, M. Agrawal and K. Sen, Combined [Formula: see text]-consecutive-[Formula: see text]-out-of-[Formula: see text]: F and consecutive-[Formula: see text]-out-of-[Formula: see text]: F systems, IEEE Trans. Reliab. 58 (2009) 328–337] where they propose an algorithm to evaluate system reliability by using the (GERT) technique, in the independent case. In this paper, we propose a new formula of the reliability of this system for nonhomogeneous Markov-dependent components. For a Combined [Formula: see text]-Consecutive-[Formula: see text]-out-of-[Formula: see text] and Consecutive-[Formula: see text]-out-of-[Formula: see text]: F System with nonhomogeneous Markov-dependent components, we derive closed-form formulas for the marginal reliability importance measure of a single component, and the joint reliability importance measure of two or more than two components using probability generating function (pgf) and conditional pgf methods.

scholarly journals Component Importance Measure Computation Method Based Fuzzy Integral with Its Application

2017 ◽  
Vol 2017 ◽  
pp. 1-18
Author(s):  
Shuai Lin ◽  
Yanhui Wang ◽  
Limin Jia ◽  
Yang Li
Keyword(s):  
System Reliability ◽  
Choquet Integral ◽  
Negative Impact ◽  
Construction Method ◽  
Centrality Measures ◽  
Importance Measure ◽  
Computation Method ◽  
Fuzzy Integral ◽  
Topological Network ◽  
Component Importance

In view of the negative impact of component importance measures based on system reliability theory and centrality measures based on complex networks theory, there is an attempt to provide improved centrality measures (ICMs) construction method with fuzzy integral for measuring the importance of components in electromechanical systems in this paper. ICMs are the meaningful extension of centrality measures and component importance measures, which consider influences on function and topology between components to increase importance measures usefulness. Our work makes two important contributions. First, we propose a novel integration method of component importance measures to define ICMs based on Choquet integral. Second, a meaningful fuzzy integral is first brought into the construction comprehensive measure by fusion multi-ICMs and then identification of important components which could give consideration to the function of components and topological structure of the whole system. In addition, the construction method of ICMs and comprehensive measure by integration multi-CIMs based on fuzzy integral are illustrated with a holistic topological network of bogie system that consists of 35 components.

scholarly journals A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components

2018 ◽  
Vol 233 (3) ◽  
pp. 328-337 ◽  
Author(s):  
Xiaoyan Zhu ◽  
Mahmoud Boushaba ◽  
Abdelmoumene Boulahia ◽  
Xian Zhao
Keyword(s):  
Closed Form ◽  
Conditional Probability ◽  
Generating Function ◽  
System Reliability ◽  
Function Method ◽  
Probability Generating Function ◽  
Importance Measure ◽  
Numerical Examples ◽  
Joint Reliability ◽  
Marginal Reliability

Consider non-homogeneous Markov-dependent components in an m-consecutive- k-out-of- n:F (G) system with sparse [Formula: see text], which consists of [Formula: see text] linearly ordered components. Two failed components are consecutive with sparse [Formula: see text] if and if there are at most [Formula: see text] working components between the two failed components, and the m-consecutive- k-out-of- n:F system with sparse [Formula: see text] fails if and if there exist at least [Formula: see text] non-overlapping runs of [Formula: see text] consecutive failed components with sparse [Formula: see text] for [Formula: see text]. We use conditional probability generating function method to derive uniform closed-form formulas for system reliability, marginal reliability importance measure, and joint reliability importance measure for such the F system and the corresponding G system. We present numerical examples to demonstrate the use of the formulas. Along with the work in this article, we summarize the work on consecutive- k systems of Markov-dependent components in terms of system reliability, marginal reliability importance, and joint reliability importance.

scholarly journals Component importance in coherent systems with exchangeable components

2015 ◽  
Vol 52 (03) ◽  
pp. 851-863 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Importance Measure ◽  
Coherent System ◽  
Coherent Systems ◽  
System A ◽  
Component Importance

This paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results.

Resilience Assessment Based on Time-Dependent System Reliability Analysis

2016 ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Assessment Method ◽  
Time Dependent ◽  
Importance Measure ◽  
System Reliability Analysis ◽  
Component Importance ◽  
System Resilience ◽  
Resilience Assessment ◽  
Time Dependent System

Significant efforts have been recently devoted to the qualitative and quantitative evaluation of resilience in engineering systems. Current resilience evaluation methods, however, have mainly focused on business supply chains and civil infrastructure, and need to be extended for application in engineering design. A new resilience metric is proposed in this paper for the design of mechanical systems to bridge this gap, by investigating the effects of recovery activity and failure scenarios on system resilience. The defined resilience metric is connected to design through time-dependent system reliability analysis. This connection enables us to design a system for a specific resilience target in the design stage. Since computationally expensive computer simulations are usually used in design, a surrogate modeling method is developed to efficiently perform time-dependent system reliability analysis for resilience assessment. System resilience assessment is then investigated based on the developed time-dependent system reliability analysis method. The connection between the proposed resilience assessment method and design is discussed through the sensitivity analysis and component importance measure. Two numerical examples are used to illustrate the effectiveness of the proposed resilience assessment method and the associated sensitivity analysis and component importance measure.

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

2013 ◽  
Vol 694-697 ◽  
pp. 907-910 ◽  
Author(s):  
Josep Franklin Sihite ◽  
Takehisa Kohda
Keyword(s):  
System Reliability ◽  
Power Transformer ◽  
Fault Tree ◽  
Importance Measure ◽  
Component Importance ◽  
Safety Improvement ◽  
System Components ◽  
Importance Analysis

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.

scholarly journals Reliability Analysis and Imprecise Component Importance Measure of Redundant Systems of OWTs Based on Component Swapping

2020 ◽  
Vol 10 (4) ◽  
pp. 1432
Author(s):  
Yao Li ◽  
Caichao Zhu ◽  
Zi Wang
Keyword(s):  
Reliability Analysis ◽  
Wind Turbines ◽  
Offshore Wind ◽  
Importance Measure ◽  
Offshore Wind Turbine ◽  
Component Reliability ◽  
Joint Reliability ◽  
Component Importance ◽  
Attractive Option ◽  
Redundant Systems

Due to the high cost of failures of wind turbines, redundancy designs are commonly applied in wind turbines for improving the reliability and availability of systems. For this reason, replacing failed components with other working components of the same type in redundant systems is becoming an attractive option of maintenance strategies towards more resilient systems. To quantitatively evaluate system’s reliability, this paper focuses on the reliability analysis of redundant systems of offshore wind turbines based on swapping existing components. The survival signature-based component swapping method is introduced to describe the new structure-function of the system upon swapping. Furthermore, the reliability model of redundant systems is established using the fault tree and survival signature. Following this, the influences of component swapping on component reliability importance measure (marginal reliability importance and joint reliability importance) without and with considerations of the imprecision of failure rates are explored. Finally, a 5MW offshore wind turbine is presented to show the applicability of the proposed approach for redundant systems, and the results show that the proposed approach can obtain realistic reliability assessment of redundant systems and considering component swapping can significantly improve system reliability.

Sign in / Sign up

Export Citation Format

Share Document