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Second-order reliability methods are commonly used for the computation of reliability, defined as the probability of satisfying an intended function in the presence of uncertainties. These methods can achieve highly accurate reliability predictions owing to a second-order approximation of the limit-state function around the Most Probable Point of failure. Although numerous formulations have been developed, the lack of full-scale comparative studies has led to a dubiety regarding the selection of a suitable method for a specific reliability analysis problem. In this study, the performance of commonly used second-order reliability methods is assessed based on the problem scale, curvatures at the Most Probable Point of failure, first-order reliability index, and limit-state contour. The assessment is based on three performance metrics: capability, accuracy, and robustness. The capability is a measure of the ability of a method to compute feasible probabilities, i.e., probabilities between 0 and 1. The accuracy and robustness are quantified based on the mean and standard deviation of relative errors with respect to exact reliabilities, respectively. This study not only provides a review of classical and novel second-order reliability methods, but also gives an insight on the selection of an appropriate reliability method for a given engineering application.

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The effects of minor elements, P, S and Si, on microstructure and mechanical properties of In 718 alloy were investigated. It is shown that decreasing P content causes the appearance of a film-like 6 phase, while increasing Si content promotes the formation of Laves and M6C phases and reduction of the precipitation of 6 phase. The most striking effect is that the stress rupture life prolonged nearly 4 times and the stress rupture ductility rose over 4 times when the P content increased from 0.0008% to 0.013%. This remarkable changes of the properties are related to the precipitation and oxidation resistance on the grain boundaries of the alloy. The mechanisms by which P, S and Si influence the superalloy are discussed in the text.

System reliability is quantified by the probability that a system performs its intended function in a period of time without failure. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method using the envelope method and second order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the existing second order component reliability method, which produces component reliability indexes. The covariance between component responses are estimated with the first order approximations, which are available from the second order approximations of the component reliability analysis. Then the joint distribution of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.