Importance Sampling for Failure Probability Estimation

Master thesis, Projectseminar, Seminar paper, Bachelor thesis

Deviations in the manufacturing process of electronic components may lead to rejections due to malfunctioning. Uncertain design parameters (i.e. geometrical and material parameters) can be modeled as random variables. Then, the failure probability of a realization can be estimated. A standard approach for estimating failure probabilities is a Monte Carlo analysis. In a Monte Carlo analysis a large number of sample points is generated according to a given probability distribution. The percentage of sample points not fulfilling some predefined performance feature specifications denotes the failure probability. In order to obtain a reliable estimation, a large number of sample points is required. This leads to high computing costs, since for each sample point a PDE must be solved, e.g. with the finite element method (FEM). Current research deals with the reduction of computational effort. Importance sampling is an approach to reduce the number of FEM evaluations by generating sample points in critical regions with a higher probability.