Glossary#

CDF#

Cumulative distribution function, denoted by \(F_X(x; \circ)\) where \(\circ\) is a placeholder for the distribution parameter(s).

FORM#

First-order reliability method

FOSM#

First-order Second-moment method

FOSPA#

First-order Saddlepoint Approximation reliability method [DS04]

ICDF#

Inverse cumulative distribution function, denoted by \(F^{-1}_X(x; \circ)\) where \(\circ\) is a placeholder for the distribution parameter(s). The domain of ICDF is \((0, 1)\). Depending on the distribution and its parameter values, the value at the boundaries may or may not be finite. ICDF is also known as the quantile function or percent point function.

IS#

Importance sampling

MCS#

Monte-Carlo simulation

PDF#

Probability density function, denoted by \(f_X(x; \circ)\) where \(\circ\) is a placeholder for the distribution parameter(s).

SORM#

Second-order reliability method

SS#

Subset simulation

SSRM#

Sequential surrogate reliability method [LGG+18]

Support#

The support of the probability density function, that is, the subset of the function domain whose elements are not mapped to zero; denoted by \(\mathcal{D}_X\).

SVM#

Support Vector Machines

References#

LGG+18

Xu Li, Chunlin Gong, Liangxian Gu, Wenkun Gao, Zhao Jing, and Hua Su. A sequential surrogate method for reliability analysis based on radial basis function. Structural Safety, 73:42–53, 2018. doi:10.1016/j.strusafe.2018.02.005.

DS04

Xiaoping Du and Agus Sudjianto. First order saddlepoint approximation for reliability analysis. AIAA Journal, 42(6):1199–1207, 2004. doi:10.2514/1.3877.