Complementary Interaction Method (CIM) for System Reliability Analysis

2007 ◽  
Author(s):  
Byeng D. Youn ◽  
Pingfeng Wang ◽  
Zhimin Xi ◽  
David J. Gorsich
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Large Scale ◽  
Higher Order ◽  
Interaction Method ◽  
Reliability Based Design ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Eigenvector Dimension Reduction ◽  
Reliability Methods

Researchers desire to evaluate system reliability uniquely and efficiently. Despite years of research, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. For system reliability bounds, the probabilities of the second or higher order joint events are assumed to be known exactly although there is no numerical method to evaluate them effectively. Two primary challenges in system reliability analysis are how to evaluate the probabilities of the second or higher order joint events and how to uniquely obtain the system reliability so that the system reliability can be used for Reliability-Based Design Optimization (RBDO). This paper proposes the Complementary Interaction Method (CIM) to define system reliability in terms of the probabilities of the component events, Ei = (X |Gi ≤ 0), and the complementary interaction events, Eij = (X |Gi*Gj ≤ 0). For large-scale systems, the probabilities of the component and complementary interaction events can be conveniently written in the CI-matrix. In this paper, three different reliability methods will be used to construct the CI-matrix numerically: First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM), and the Eigenvector Dimension Reduction (EDR) method. Two examples will be employed to demonstrate that the CIM with the EDR method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

Complementary Intersection Method for System Reliability Analysis

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Byeng D. Youn ◽  
Pingfeng Wang
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
High Efficiency ◽  
Second Order ◽  
Approximation Formula ◽  
Joint Failure ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Reliability Methods ◽  
Intersection Method

Although researchers desire to evaluate system reliability accurately and efficiently over the years, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. However, two primary challenges are as follows: (1) Most numerical methods cannot effectively evaluate the probabilities of the second (or higher)–order joint failure events with high efficiency and accuracy, which are needed for system reliability evaluation and (2) there is no unique system reliability approximation formula, which can be evaluated efficiently with commonly used reliability methods. Thus, this paper proposes the complementary intersection (CI) event, which enables us to develop the complementary intersection method (CIM) for system reliability analysis. The CIM expresses the system reliability in terms of the probabilities of the CI events and allows the use of commonly used reliability methods for evaluating the probabilities of the second–order (or higher) joint failure events efficiently. To facilitate system reliability analysis for large-scale systems, the CI-matrix can be built to store the probabilities of the first- and second-order CI events. In this paper, three different numerical solvers for reliability analysis will be used to construct the CI-matrix numerically: first-order reliability method, second-order reliability method, and eigenvector dimension reduction (EDR) method. Three examples will be employed to demonstrate that the CIM with the EDR method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

System Reliability Analysis With Second Order Saddlepoint Approximation

2019 ◽  
Author(s):  
Hao Wu ◽  
Xiaoping Du
Keyword(s):  
Normal Distribution ◽  
Reliability Analysis ◽  
System Reliability ◽  
Multivariate Normal Distribution ◽  
High Efficiency ◽  
Saddlepoint Approximation ◽  
Second Order ◽  
Multivariate Normal ◽  
System Reliability Analysis ◽  
Reliability Method

Abstract The second order saddlepoint approximation (SPA) has been used for component reliability analysis for higher accuracy than the traditional second order reliability method. This work extends the second order SPA to system reliability analysis. The joint distribution of all the component responses is approximated by a multivariate normal distribution. To maintain high accuracy of the approximation, the proposed method employs the second order SPA to accurately generate the marginal distributions of component responses; to simplify computations and achieve high efficiency, the proposed method estimates the covariance matrix of the multivariate normal distribution with the first order approximation to component responses. Examples demonstrate the high effectiveness of the second order SPA method for system reliability analysis.

Time-Dependent System Reliability Analysis Using Random Field Discretization

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Random Field ◽  
Reliability Analysis ◽  
System Reliability ◽  
Probability Of Failure ◽  
Two Dimensions ◽  
Time Dependent ◽  
Time Interval ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Time Dependent System

This paper proposes a novel and efficient methodology for time-dependent system reliability analysis of systems with multiple limit-state functions of random variables, stochastic processes, and time. Since there are correlations and variations between components and over time, the overall system is formulated as a random field with two dimensions: component index and time. To overcome the difficulties in modeling the two-dimensional random field, an equivalent Gaussian random field is constructed based on the probability equivalency between the two random fields. The first-order reliability method (FORM) is employed to obtain important features of the equivalent random field. By generating samples from the equivalent random field, the time-dependent system reliability is estimated from Boolean functions defined according to the system topology. Using one system reliability analysis, the proposed method can get not only the entire time-dependent system probability of failure curve up to a time interval of interest but also two other important outputs, namely, the time-dependent probability of failure of individual components and dominant failure sequences. Three examples featuring series, parallel, and combined systems are used to demonstrate the effectiveness of the proposed method.

A robust system reliability analysis using partitioning and parallel processing of Markov chain

2014 ◽  
Vol 28 (4) ◽  
pp. 311-322 ◽  
Author(s):  
Po Ting Lin ◽  
Yu-Cheng Chou ◽  
Yung Ting ◽  
Shian-Shing Shyu ◽  
Chang-Kuo Chen
Keyword(s):  
Markov Chain ◽  
Parallel Processing ◽  
Reliability Analysis ◽  
System Reliability ◽  
Large Scale ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Processing Unit ◽  
Central Processing ◽  
System Reliability Analysis

AbstractThis paper presents a robust reliability analysis method for systems of multimodular redundant (MMR) controllers using the method of partitioning and parallel processing of a Markov chain (PPMC). A Markov chain is formulated to represent the N distinct states of the MMR controllers. Such a Markov chain has N2 directed edges, and each edge corresponds to a transition probability between a pair of start and end states. Because N can be easily increased substantially, the system reliability analysis may require large computational resources, such as the central processing unit usage and memory occupation. By the PPMC, a Markov chain's transition probability matrix can be partitioned and reordered, such that the system reliability can be evaluated through only the diagonal submatrices of the transition probability matrix. In addition, calculations regarding the submatrices are independent of each other and thus can be conducted in parallel to assure the efficiency. The simulation results show that, compared with the sequential method applied to an intact Markov chain, the proposed PPMC can improve the performance and produce allowable accuracy for the reliability analysis on large-scale systems of MMR controllers.

System Reliability Analysis With Second-Order Saddlepoint Approximation

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Hao Wu ◽  
Xiaoping Du
Keyword(s):  
Normal Distribution ◽  
Reliability Analysis ◽  
System Reliability ◽  
Multivariate Normal Distribution ◽  
High Efficiency ◽  
Saddlepoint Approximation ◽  
Second Order ◽  
Multivariate Normal ◽  
System Reliability Analysis ◽  
Reliability Method

Abstract The second-order saddlepoint approximation (SOSPA) has been used for component reliability analysis for higher accuracy than the traditional second-order reliability method (SORM). This work extends the second-order saddlepoint approximation (SPA) to system reliability analysis. The joint distribution of all the component responses is approximated by a multivariate normal distribution. To maintain high accuracy of the approximation, the proposed method employs the second-order SPA to accurately generate the marginal distributions of the component responses; to simplify computations and achieve high efficiency, the proposed method estimates the covariance matrix of the multivariate normal distribution with the first-order approximation to the component responses. Examples demonstrate the high effectiveness of the second-order SPA method for system reliability analysis.

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