In this paper, two second-order methods are proposed for reliability analysis. First, general random variables are transformed to standard normal random variables. Then, the limit-state function is additively decomposed into one-dimensional functions, which are then expanded at the mean-value point to second-order terms. The approximated limit-state function becomes the sum of independent variables following noncentral chi-square distributions or normal distributions. The first method computes the probability of failure by the saddle-point approximation. If a saddle-point does not exist, the second method is then used. The second method approximates the limit-state function by a quadratic function with independent variables following normal distributions with the same variances. This treatment leads to a quadratic function that follows a noncentral chi-square distribution. These methods generally produce more accurate reliability approximations than the first-order reliability method (FORM) with 2n + 1 function evaluations, where n is the dimension of the problem. The effectiveness of the proposed methods is demonstrated with three examples, and the proposed methods are compared with the first- and second-order reliability methods (SROMs).

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# Reliability Analysis by Mean-Value Second-Order Expansion

Deshun Liu

,
Deshun Liu

Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment,

liudeshun@hnust.edu.cn
Hunan University of Science and Technology

, Xiangtan, Hunan 411201, P. R. China

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Yehui Peng

Yehui Peng

School of Mathematics and Computational Science,

pengyehui@yahoo.com.cn
Hunan University of Science and Technology

, Xiangtan, Hunan 411201, P. R. China

Search for other works by this author on:

Deshun Liu

Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment,

Hunan University of Science and Technology

, Xiangtan, Hunan 411201, P. R. China

liudeshun@hnust.edu.cn

Yehui Peng

School of Mathematics and Computational Science,

Hunan University of Science and Technology

, Xiangtan, Hunan 411201, P. R. China

pengyehui@yahoo.com.cn

*J. Mech. Des*. Jun 2012, 134(6): 061005 (8 pages)

**Published Online:**April 27, 2012

Article history

Received:

April 30, 2011

Revised:

March 28, 2012

Online:

April 27, 2012

Published:

April 27, 2012

Citation

Liu, D., and Peng, Y. (April 27, 2012). "Reliability Analysis by Mean-Value Second-Order Expansion." ASME. *J. Mech. Des*. June 2012; 134(6): 061005. https://doi.org/10.1115/1.4006528

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