Time-Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals

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A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis (2016, methodology): “For instance, a PHI2 method has been developed to compute the time-variant reliability by estimating the upcrossing rate at each time instant [6]; Singh and Mourelatos [7] proposed a composite limit-state function method and investigated importance sampling [8], Markov Chain Monte Carlo simulation (”
Time-Dependent System Reliability Analysis Using Random Field Discretization (2015, methodology): “Methods falling into the third group are the adaptive importance sampling approach [11], Markov chain Monte Carlo simulation [12], and first-order sampling approach [13].”
First order reliability method for time-variant problems using series expansions (2015, background): “It is the derivative of the first time to failure (FTTF) TF (Singh et al. 2010; Hu and Du 2013c; Wang et al. 2013). v1(t) can also be viewed as the first-time-upcrossing rate. v1(t) is given by v1(t) = lim t→0 Pr{ t < TF < t + t |Tf > t} t (29) To calculate v1(t), we also define an indicator I1(t)…”