Saddlepoint approximation reliability method for quadratic functions in normal variables

[1]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[2]  H. Daniels.  Saddlepoint Approximations in Statistics , 1954 .

[3]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[4]  S. Rice,et al.  Saddle point approximation for the distribution of the sum of independent random variables , 1980, Advances in Applied Probability.

[5]  R. Rackwitz,et al.  Non-Normal Dependent Vectors in Structural Safety , 1981 .

[6]  R. Rackwitz,et al.  First-order concepts in system reliability , 1982 .

[7]  K. Breitung.  Asymptotic approximations for multinormal integrals , 1984 .

[8]  Johann Arbocz,et al.  First-order second-moment analysis of the buckling of shells with Random imperfections , 1987 .

[9]  A. Kiureghian,et al.  Second-Order Reliability Approximations , 1987 .

[10]  H. E. Daniels,et al.  Tail Probability Approximations , 1987 .

[11]  R. Rackwitz,et al.  New light on first- and second-order reliability methods , 1987 .

[12]  Arjun K. Gupta,et al.  Asymptotic expansions for the distribution of quadratic forms in normal variables , 1988 .

[13]  L. Tvedt.  Distribution of quadratic forms in normal space-application to structural reliability , 1990 .

[14]  H. U. Köylüoglu,et al.  New Approximations for SORM Integrals , 1994 .

[15]  Henrik O. Madsen,et al.  Structural Reliability Methods , 1996 .

[16]  A. Kiureghian,et al.  Multiple design points in first and second-order reliability , 1998 .

[17]  George Casella,et al.  Explaining the Saddlepoint Approximation , 1999 .

[18]  Yan-Gang Zhao,et al.  A general procedure for first/second-order reliabilitymethod (FORM/SORM) , 1999 .

[19]  Yan-Gang Zhao,et al.  New Approximations for SORM: Part 2 , 1999 .

[20]  Xiaoping Du,et al.  Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design , 2004, DAC 2002.

[21]  Hisashi Tanizaki,et al.  Computational methods in statistics and econometrics , 2004 .

[22]  Xiaoping Du,et al.  A Saddlepoint Approximation Method for Uncertainty Analysis , 2004, DAC 2004.

[23]  A. Sudjianto,et al.  Reliability-Based Design With the Mixture of Random and Interval Variables , 2005, DAC 2003.

[24]  Ramana V. Grandhi,et al.  Reliability-based Structural Design , 2006 .

[25]  Niels C. Lind,et al.  Methods of structural safety , 2006 .

[26]  Jia Guo,et al.  Sequential optimization and reliability assessment for multidisciplinary systems design , 2008 .

[27]  Xiaoping Du,et al.  Saddlepoint Approximation for Sequential Optimization and Reliability Analysis , 2008 .

[28]  Sankaran Mahadevan,et al.  Design Optimization With System-Level Reliability Constraints , 2008 .

[29]  Xiaoping Du,et al.  A Second-Order Reliability Method With First-Order Efficiency , 2010 .

[30]  K. Choi,et al.  System reliability-based design optimization using the MPP-based dimension reduction method , 2010 .

[31]  Rami Mansour,et al.  A Closed-Form Second-Order Reliability Method Using Noncentral Chi-Squared Distributions , 2014 .

[32]  Xiaoping Du,et al.  A Random Field Approach to Reliability Analysis With Random and Interval Variables , 2015 .