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.

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.

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.

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.

Time-Dependent System Reliability Analysis With Second-Order Reliability Method

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Hao Wu ◽  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Second Order ◽  
Time Dependent ◽  
Component Reliability ◽  
Reliability Method ◽  
Series Systems ◽  
State Functions ◽  
Time Dependent System

Abstract System reliability is quantified by the probability that a system performs its intended function in a period of time without failures. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method using the envelope method and second-order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the second-order component reliability method with an improve envelope approach, which produces a component reliability index. The covariance between component responses is estimated with the first-order approximations, which are available from the second-order approximations of the component reliability analysis. Then, the joint distribution of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

Time-Dependent System Reliability Analysis With Second Order Reliability Method

2020 ◽  
Author(s):  
Hao Wu ◽  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Second Order ◽  
Time Dependent ◽  
Component Reliability ◽  
Reliability Method ◽  
Series Systems ◽  
State Functions ◽  
Time Dependent System

Abstract System reliability is quantified by the probability that a system performs its intended function in a period of time without failure. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method that uses the envelop method and second order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the existing second order component reliability method, which produces component reliability indexes. The covariance between components responses are estimated with the first order approximations, which are available from the second order approximations of the component reliability analysis. Then the joint probability of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

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