Probability, Reliability and Statistical Methods in Engineering Design
Citations
479 citations
Cites background from "Probability, Reliability and Statis..."
...Several texts and review papers provide overviews of approaches to sensitivity analysis for engineering applications [25,26], including biomechanics [19]....
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294 citations
Cites methods from "Probability, Reliability and Statis..."
...There are many methods for calculating the failure probability of a system [22-24]....
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203 citations
Cites methods from "Probability, Reliability and Statis..."
...When considering reliability, discontinuities might also hamper the use of approximation methods such as first and second order reliability methods (FORM and SORM) [9], advanced mean value (AMV) [10], or Monte-Carlo simulations with response surfaces....
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197 citations
Cites background from "Probability, Reliability and Statis..."
...finite element models) or response surface approximations, for a large variety of engineering problems [16]....
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193 citations
Cites background or methods from "Probability, Reliability and Statis..."
...Note that a relatively larger error of the adaptive probability analysis occurs near 10% and 90%, which is mainly due to the error of FORM....
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...Note that a relatively larger amount of error of the adaptive probability analysis occurs between 50% and 95%, which is again mainly due to the error of FORM....
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...The probability distribution function is obtained by identifying the propagation of input uncertainty to output 3 uncertainty as (Madsen et al. 1986; Haldar and Mahadevan 2000) FG(g) = ∞∫ −∞ · · · ∞∫ −∞ fX(x)dx1 . . . dxn (1) where the uncertainty FX(x) (or fX(x)) of input X is propagated to the…...
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...Using FORM, (2) or (3) can be solved by formulating an optimization with one equality constraint (Tu and Choi 1999; Youn et al. 2001, 2003; Lee and Kwak 1987– 88) to obtain gi = g(u ∗ i ), if βi > 0 , maximize G(U) subject to ‖U‖= βi , for i= 1, . . . ,NPL if βi < 0 , minimize G(U) subject to ‖U‖= βi , for i= 1, . . . ,NPL (5) TS b Please check quality of all your figures send higher resolution versions of Figs....
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...This is referred to as the first-order reliability method (FORM) (Hasofer and Lind 1974; Madsen et al. 1986; Haldar and Mahadevan 2000), as shown in Fig....
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References
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