Choi,
S.-K.
,
Grandhi,
R.
, and
Canfield,
R. A.
, 2006, Reliability-Based Structural Design,
Springer Science & Business Media, New York.

Elishakoff,
I.
,
Van Manen,
S.
, and
Arbocz,
J.
, 1987, “
First-Order Second-Moment Analysis of the Buckling of Shells With Random Imperfections,” AIAA J.,
25(8), pp. 1113–1117.

[CrossRef]
Mahadevan,
S.
, and
Haldar,
A.
, 2000, Probability, Reliability and Statistical Method in Engineering Design,
Wiley,
New York.

Hohenbichler,
M.
, and
Rackwitz,
R.
, 1983, “
First-Order Concepts in System Reliability,” Struct. Saf.,
1(3), pp. 177–188.

[CrossRef]
Breitung,
K.
, 1984, “
Asymptotic Approximations for Multinormal Integrals,” J. Eng. Mech.,
110(3), pp. 357–366.

[CrossRef]
Tvedt, L.
, 1983, “
Two Second-Order Approximations to the Failure Probability,” Det Norske Veritas, Hovik, Norway, Report No. RDIV/20-004-83.

Tvedt,
L.
, 1990, “
Distribution of Quadratic Forms in Normal Space-Application to Structural Reliability,” J. Eng. Mech.,
116(6), pp. 1183–1197.

[CrossRef]
Zhao,
Y.-G.
, and
Ono,
T.
, 1999, “
New Approximations for SORM—Part 1,” J. Eng. Mech.,
125(1), pp. 79–85.

[CrossRef]
Madsen,
H. O.
,
Krenk,
S.
, and
Lind,
N. C.
, 2006, Methods of Structural Safety, Dover Publications, Mineola, NY.

Ditlevsen,
O.
, and
Madsen,
H. O.
, 1996, Structural Reliability Methods,
Wiley,
New York.

Mansour,
R.
, and
Olsson,
M.
, 2014, “
A Closed-Form Second-Order Reliability Method Using Noncentral Chi-Squared Distributions,” ASME J. Mech. Des.,
136(10), p. 101402.

[CrossRef]
Laman,
J. A.
, and
Nowak,
A. S.
, 1996, “
Fatigue-Load Models for Girder Bridges,” J. Struct. Eng.,
122(7), pp. 726–733.

[CrossRef]
Haider,
S. W.
,
Harichandran,
R. S.
, and
Dwaikat,
M. B.
, 2008, “
Estimating Bimodal Distribution Parameters and Traffic Levels From Axle Load Spectra,” Transportation Research Board 87th Annual Meeting, Washington, DC, Jan. 13–17, Paper No. 08-0824.

https://trid.trb.org/view/847690
Haider,
S. W.
,
Harichandran,
R. S.
, and
Dwaikat,
M. B.
, 2009, “
Closed-Form Solutions for Bimodal Axle Load Spectra and Relative Pavement Damage Estimation,” J. Transp. Eng.,
135(12), pp. 974–983.

[CrossRef]
Mones,
E.
,
Araújo,
N. A.
,
Vicsek,
T.
, and
Herrmann,
H. J.
, 2014, “
Shock Waves on Complex Networks,” Sci. Reports,
4(1), p. 4949.

Hu, Z.
, and
Du, X.
, 2018, “
Saddlepoint Approximation Reliability Method for Quadratic Functions in Normal Variables,” Struct. Saf.,
71, pp. 24–32.

Daniels,
H. E.
, 1987, “
Tail Probability Approximations,” Int. Stat. Rev.,
1, pp. 37–48.

[CrossRef]
Goutis,
C.
, and
Casella,
G.
, 1999, “
Explaining the Saddlepoint Approximation,” Am. Stat.,
53(3), pp. 216–224.

Du,
X.
, and
Sudjianto,
A.
, 2004, “
A Saddlepoint Approximation Method for Uncertainty Analysis,” ASME Paper No. DETC2004-57269.

Du,
X.
, 2008, “
Saddlepoint Approximation for Sequential Optimization and Reliability Analysis,” ASME J. Mech. Des.,
130(1), p. 011011.

[CrossRef]
Huang,
B.
, and
Du,
X.
, 2008, “
Probabilistic Uncertainty Analysis by Mean-Value First-Order Saddlepoint Approximation,” Reliab. Eng. Syst. Saf.,
93(2), pp. 325–336.

[CrossRef]
Meng,
D.
,
Huang,
H.-Z.
,
Wang,
Z.
,
Xiao,
N.-C.
, and
Zhang,
X.-L.
, 2014, “
Mean-Value First-Order Saddlepoint Approximation Based Collaborative Optimization for Multidisciplinary Problems Under Aleatory Uncertainty,” J. Mech. Sci. Technol.,
28(10), pp. 3925–3935.

[CrossRef]
Du,
X.
, and
Sudjianto,
A.
, 2004, “
First-Order Saddlepoint Approximation for Reliability Analysis,” AIAA J.,
42(6), pp. 1199–1207.

[CrossRef]
Dolinski,
K.
, 1982, “
First-Order Second-Moment Approximation in Reliability of Structural Systems: Critical Review and Alternative Approach,” Struct. Saf.,
1(3), pp. 211–231.

[CrossRef]
Lee,
T. W.
, and
Kwak,
B. M.
, 1987, “
A Reliability-Based Optimal Design Using Advanced First Order Second Moment Method,” J. Struct. Mech.,
15(4), pp. 523–542.

Du,
X.
, and
Chen,
W.
, 2004, “
Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design,” ASME J. Mech. Des.,
126(2), pp. 225–233.

[CrossRef]
Du,
X.
,
Guo,
J.
, and
Beeram,
H.
, 2008, “
Sequential Optimization and Reliability Assessment for Multidisciplinary Systems Design,” Struct. Multidiscip. Optim.,
35(2), pp. 117–130.

[CrossRef]
Lee,
I.
,
Choi,
K.
, and
Gorsich,
D.
, 2010, “
System Reliability-Based Design Optimization Using the MPP-Based Dimension Reduction Method,” Struct. Multidiscip. Optim.,
41(6), pp. 823–839.

[CrossRef]
McDonald,
M.
, and
Mahadevan,
S.
, 2008, “
Design Optimization With System-Level Reliability Constraints,” ASME J. Mech. Des.,
130(2), p. 021403.

[CrossRef]
Rosenblatt,
M.
, 1952, “
Remarks on a Multivariate Transformation,” Ann. Math. Stat.,
23(3), pp. 470–472.

[CrossRef]
Stockholm,
F. E.
, 1932, “
On the Probability Function in the Collective Theory of Risk,” Skand. Aktuarietidskrift,
15(3), pp. 175–195.

Lugannani,
R.
, and
Rice,
S.
, 1980, “
Saddle Point Approximation for the Distribution of the Sum of Independent Random Variables,” Adv. Appl. Probab.,
12(2), pp. 475–490.

[CrossRef]
Zhang,
J.
, and
Du,
X.
, 2010, “
A Second-Order Reliability Method With First-Order Efficiency,” ASME J. Mech. Des.,
132(10), p. 101006.

[CrossRef]
Alibrandi,
U.
,
Alani,
A.
, and
Koh,
C.
, 2015, “
Implications of High-Dimensional Geometry for Structural Reliability Analysis and a Novel Linear Response Surface Method Based on SVM,” Int. J. Comput. Methods,
12(4), p. 1540016.

[CrossRef]
Hurtado,
J. E.
, 2012, “
Dimensionality Reduction and Visualization of Structural Reliability Problems Using Polar Features,” Probab. Eng. Mech.,
29, pp. 16–31.

[CrossRef]
Katafygiotis,
L. S.
, and
Zuev,
K. M.
, 2008, “
Geometric Insight Into the Challenges of Solving High-Dimensional Reliability Problems,” Probab. Eng. Mech.,
23(2–3), pp. 208–218.

[CrossRef]
Valdebenito,
M.
,
Pradlwarter,
H.
, and
Schuëller,
G.
, 2010, “
The Role of the Design Point for Calculating Failure Probabilities in View of Dimensionality and Structural Nonlinearities,” Struct. Saf.,
32(2), pp. 101–111.

[CrossRef]
Alibrandi,
U.
,
Alani,
A. M.
, and
Ricciardi,
G.
, 2015, “
A New Sampling Strategy for SVM-Based Response Surface for Structural Reliability Analysis,” Probab. Eng. Mech.,
41, pp. 1–12.

[CrossRef]
Hurtado,
J. E.
, and
Alvarez,
D. A.
, 2010, “
An Optimization Method for Learning Statistical Classifiers in Structural Reliability,” Probab. Eng. Mech.,
25(1), pp. 26–34.

[CrossRef]
Gander,
W.
, and
Gautschi,
W.
, 2000, “
Adaptive Quadrature—Revisited,” BIT Numer. Math.,
40(1), pp. 84–101.

[CrossRef]
Malcolm,
M. A.
, and
Simpson,
R. B.
, 1975, “
Local Versus Global Strategies for Adaptive Quadrature,” ACM Trans. Math. Software (TOMS),
1(2), pp. 129–146.

[CrossRef]
Song,
S.
,
Lu,
Z.
, and
Qiao,
H.
, 2009, “
Subset Simulation for Structural Reliability Sensitivity Analysis,” Reliab. Eng. Syst. Saf.,
94(2), pp. 658–665.

[CrossRef]
Zhao,
H.
,
Yue,
Z.
,
Liu,
Y.
,
Gao,
Z.
, and
Zhang,
Y.
, 2015, “
An Efficient Reliability Method Combining Adaptive Importance Sampling and Kriging Metamodel,” Appl. Math. Modell.,
39(7), pp. 1853–1866.

[CrossRef]
Hu,
Z.
, and
Mahadevan,
S.
, 2016, “
Global Sensitivity Analysis-Enhanced Surrogate (GSAS) Modeling for Reliability Analysis,” Struct. Multidiscip. Optim.,
53(3), pp. 501–521.

[CrossRef]