Failure Domain Analysis Using Sliced-Normal Distributions

Sliced-normal (SN) distributions enable characterization of parameters exhibiting complex dependencies with minimal modeling effort. We leverage the semialgebraic nature of SN distributions to identify the most likely points of failure (MLPs) corresponding to a given failure domain. When this domain is semialgebraic, Sum of Squares (SOS) optimization is used to guarantee that no MLPs are missed within a region of interest. The MLPs not only enable the identification of all the critical points of failure, but also the efficient estimation of failure probabilities using Importance Sampling (IS). The IS density is constructed as a Gaussian Mixture (GM) model with means at the MLPs and covariances equal to the weighted empirical covariance of sample sets drawn in the vicinity of the MLPs.

Keywords: Importance sampling, Reliability analysis, Failure estimation, Parameter dependency, Semidefinite programming, Gaussian mixture.

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