Analysis of approximations for multinormal integration in system reliability computation

Structural Safety

Volumn 28, Issue 4, 2006, Pages 361-377

  Yuan, X X ^a   Pandey, M D ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Conditional distributions; First order reliability method; Multinormal integrals; Probability theory; Series and parallel systems; System reliability

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; FAILURE (MECHANICAL); FAILURE ANALYSIS; INTEGRATION; PROBABILITY; RELIABILITY;

CONDITIONAL DISTRIBUTIONS; FIRST-ORDER RELIABILITY METHOD; MULTINORMAL INTEGRALS; PRODUCT OF CONDITIONAL MARGINAL (PCM) METHOD; SYSTEM RELIABILITY; SYSTEM RELIABILITY COMPUTATION;

SYSTEMS ANALYSIS;

APPROXIMATION THEORY; ERROR ANALYSIS; FAILURE (MECHANICAL); FAILURE ANALYSIS; INTEGRATION; PROBABILITY; RELIABILITY; SYSTEMS ANALYSIS;

EID: 33745223060     PISSN: 01674730     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.strusafe.2005.10.002     Document Type: Article

References (12)

1. Hohenbichler M., and Rackwitz R. First-order concepts in system reliability. Struct Saf 1 (1983) 177-188
2. Gollwitzer S., and Rackwitz R. An efficient numerical solution to the multinormal integral. Probabilist Eng Mech 3 2 (1988) 98-101
3. Tang L.K., and Melchers R.E. Improved approximation for multinormal integrals. Struct Saf 4 (1987) 81-93
4. Ambartzumian R., Der Kiureghian A., Ohanian V., and Sukiasian H. Multinormal probability by sequential conditioned importance sampling: theory and application. Probabilist Eng Mech 13 4 (1998) 299-308
5. Melchers R.E. Structural reliability: analysis and prediction. 2nd ed. (1999), Wiley, Chichester, UK
6. Pandey M.D. An effective approximation to evaluate multinormal integrals. Struct Saf 20 (1998) 51-67
7. Pandey M.D., and Sarkar A. Comparison of a simple approximation for multinormal integration with an importance sampling-based simulation method. Probabilist Eng Mech 17 (2002) 215-218
8. Pandey M.D. A simple approach to multinormal integration with applications to the system reliability computation. J Civil Eng Environ Syst 15 (1997) 89-105
9. Mori Y., and Kato T. Multinormal integrals by importance sampling for series system reliability. Struct Saf 25 (2003) 363-378
10. Tallis G.M. The moment generating function of the truncated multi-normal distribution. J Royal Statist Soc, Ser B 23 (1961) 223-229
11. Birnbaum Z.W. Effect of linear truncation on a multinormal population. Ann Math Statist 21 (1950) 272-279
12. Kotz S., Balakrishnan N., and Johnson N.L. Continuous multivariate distributions vol. 1: models and applications. 2nd ed. (2000), Wiley