Bounds on System Reliability by Linear Programming

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Component and system reliability-based topology optimization using a single-loop method (2010, methodology): “To circumvent this difficulty, several methods have been developed to estimate bounds for the system reliability (Hohenbichler and Rackwitz 1983; Song and Kiureghian 2003; Song and Kang 2007 ;Z hao et al. 2007).”
Joint First-Passage Probability and Reliability of Systems under Stochastic Excitation (2006, methodology): “Bounds on the reliability of the entire system are then obtained by use of LP Song and Der Kiureghian 2003, employing the marginal and joint component fragilities.”
System reliability analysis with saddlepoint approximation (2010, methodology): “Other approximation methods include the use of Linear Programming ( Song and Kiureghian 2003 ) and the complementary intersection method with eigenvector dimension reduction (Youn and Wang 2009).”
Rock Wedge Stability Analysis Using System Reliability Methods (2007, methodology): “Finally, bounds of the probability of failure of the system may be obtained using, for instance, the linear programming (LP) approach proposed by Song and Der Kiureghian (2003) .”