Recommended Texts and References

This page lists commonly used references for reliability methods and probabilistic analysis.

Ang, A. H.-S., and Tang, W. H. (2007). Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering (2nd ed.). John Wiley and Sons.
Der Kiureghian, A. (2022). Structural and System Reliability. Cambridge University Press.
Robert, Christian P., and Casella, George. (2004). Monte Carlo Statistical Methods. Springer New York.
Sorensen, John Dalsgaard. (2004). Notes in Structural Reliability Theory and Risk Analysis. Aalborg, February 2004. ->

Additional References Used in Documentation

These references are cited in worked examples, method notes, and profile options across the documentation.

Au, S. K., and Beck, J. L. (1999). A new adaptive importance sampling scheme for reliability calculations. ->
Chan, C. L., and Low, B. K. (2011/2012). Practical second-order reliability analysis applied to foundation engineering. ->

Hu, Z., and Du, X. (2018). Efficient reliability-based design with second-order approximations. Engineering Optimization, 50(1), 101-119. ->
Ji, B., Kodikara, J. K., and Li, H. (2024). Robust reliability-based design approach by inverse FORM with adaptive conjugate search algorithm. ->
Sorensen, John Dalsgaard. (2004). Notes in Structural Reliability Theory and Risk Analysis. Aalborg, February 2004. ->

Breitung, K. (1984). Asymptotic approximations for multinormal integrals. ->
Der Kiureghian, A., Lin, H.-Z., and Hwang, S.-J. (1987). Second-order reliability approximations. ->
Du, X., and Sudjianto, A. (2004). A saddlepoint approximation method for uncertainty analysis. ->
Hohenbichler, M., and Rackwitz, R. (1988). Improvement of second-order reliability estimates by importance sampling. ->
Hu, Z., and Du, X. (2018). Saddlepoint approximation reliability method for quadratic functions in normal variables. ->
Koyluoglu, H. U., and Nielsen, S. R. K. (1994). New approximations for SORM integrals. ->
Tvedt, L. (1990). Distribution of quadratic forms in normal space: application to structural reliability. ->
Zhao, Y.-G., and Ono, T. (1999a). New approximations for SORM: Part 1. ->
Zhao, Y.-G., and Ono, T. (1999b). New approximations for SORM: Part 2. ->

Cotter, S. L., Roberts, G. O., Stuart, A. M., and White, D. (2013). MCMC methods for functions: modifying old algorithms to make them faster. ->
Roberts, G. O., and Rosenthal, J. S. (2007). Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms. ->
Xiao, S., and Nowak, W. (2022). Reliability sensitivity analysis based on a two-stage Markov chain Monte Carlo simulation. ->

Rebonato, R., and Jaeckel, P. (2011). The most general methodology to create a valid correlation matrix for risk management and option pricing purposes. -> (DOI)

For software package citations and dependency-level references, see the Software References pages in the documentation.