Reliability estimation using unscented transformation

In this paper, we consider the problem of fast reliability analysis with focus on mean and covariance for large-scale systems that consist of components with not necessarily exponential and possibly cross-correlated failure statistics. For its solution we propose to use the unscented transformation, an error-bounded deterministic sampling method known from filter theory. The estimation problem is approached from two different directions. From one perspective, the mean and variance of the system survival probability are estimated for a fixed time instant, whereas from the other perspective, mean and covariance of the failure times are estimated. The main difference between these perspectives is that the former is numerically better behaved than the latter. An example illustrates these methods.