Methods for Time‐Dependent Reliability and Sensitivity Analysis

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Abstract
A general and efficient method for reliability and sensitivity analysis is presented. The methods are for the analysis of components and systems in design situations where uncertainties are represented by a vector of random variables and a stationary Gaussian vector process. A formulation as a first‐passage problem for a vector process outcrossing a safe set is first applied for a fixed value of the random variable vector. This gives a conditional failure probability, and a fast integration technique based on a first‐ or second‐order reliability method is then applied to compute the unconditional failure probability. Extensive use of analytical gradient information is made in the iteration algorithms and in the calculation of sensitivity factors. A nested first‐order reliability method is proposed together with a method based on an integrated optimization for the two first‐order reliability analyses. For a preliminary analysis, a “crude” first‐order reliability method is described. The computation time is only a few times the computation time for a first‐order reliability analysis of a similar time‐independent problem. Software developed from existing special software for first‐order reliability analysis or existing general optimization software can be applied.

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